<PAGE>   1
 
   AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON DECEMBER 12, 1997
================================================================================
 
                                   FORM 10-Q
 
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
(MARK ONE)
 
[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
    SECURITIES EXCHANGE ACT OF 1934
 
     FOR THE QUARTERLY PERIOD ENDED OCTOBER 31, 1997
 
                                       OR
 
[  ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
     SECURITIES EXCHANGE ACT OF 1934
 
                         COMMISSION FILE NUMBER 1-3998
 
                            LITTON INDUSTRIES, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                                  <C>
                     DELAWARE                                       95-1775499
          (STATE OR OTHER JURISDICTION OF                        (I.R.S. EMPLOYER
          INCORPORATION OR ORGANIZATION)                       IDENTIFICATION NO.)
 
21240 BURBANK BOULEVARD, WOODLAND HILLS, CALIFORNIA                 91367-6675
     (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                       (ZIP CODE)
</TABLE>
 
       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (818) 598-5000
 
     Indicate by check mark whether the Registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  Yes [X]  No [ ]
 
     On November 28, 1997 there were 46,040,503 shares of Common Stock
outstanding.
 
                                  Page 1 of 10
                        Exhibit Index appears on Page 8.
 
================================================================================
<PAGE>   2
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                                     INDEX
 
                              REPORT ON FORM 10-Q
 
                       FOR QUARTER ENDED OCTOBER 31, 1997
 
<TABLE>
<CAPTION>
                                                                                        PAGE
                                                                                       NUMBER
                                                                                       ------
<S>         <C>                                                                        <C>
PART I. FINANCIAL INFORMATION
  Item 1.   Financial Statements
            Consolidated Statements of Operations
              Three months ended October 31, 1997 and 1996...........................      3
            Consolidated Balance Sheets
              October 31, 1997 and July 31, 1997.....................................      4
            Consolidated Statements of Cash Flows
              Three months ended October 31, 1997 and 1996...........................      5
            Notes to Consolidated Financial Statements...............................      6
  Item 2.   Management's Discussion and Analysis of Financial Condition and Results        
              of Operations..........................................................      7
 
PART II. OTHER INFORMATION
  Item 6.   Exhibits and Reports on Form 8-K.........................................      8
 
Signature............................................................................     10
</TABLE>
 
                                        2
<PAGE>   3

                         PART I. FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS

                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                (THOUSANDS OF DOLLARS, EXCEPT PER SHARE AMOUNTS)
 
<TABLE>
<CAPTION>
                                                                         THREE MONTHS ENDED
                                                                             OCTOBER 31,
                                                                      -------------------------
                                                                         1997           1996
                                                                      ----------     ----------
<S>                                                                   <C>            <C>
Sales and Service Revenues..........................................  $1,039,035     $1,048,877
                                                                      ----------     ----------
Costs and Expenses
  Cost of sales.....................................................     800,017        824,787
  Selling, general and administrative...............................     121,991        112,276
  Depreciation and amortization.....................................      34,388         34,165
  Interest -- net...................................................      10,231         11,305
                                                                      ----------     ----------
          Total.....................................................     966,627        982,533
                                                                      ----------     ----------
Earnings before Taxes on Income.....................................      72,408         66,344
Taxes on Income.....................................................     (28,963)       (26,538)
                                                                      ----------     ----------
          Net Earnings..............................................  $   43,445     $   39,806
                                                                      ==========     ==========
 
Primary Earnings per Share..........................................  $     0.92     $     0.83
                                                                      ==========     ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                        3
<PAGE>   4
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                          CONSOLIDATED BALANCE SHEETS
                             (THOUSANDS OF DOLLARS)
 
<TABLE>
<CAPTION>
                                                                      OCTOBER 31,     JULY 31,
                                                                         1997           1997
                                                                      ----------     ----------
<S>                                                                   <C>            <C>
ASSETS
Current Assets
  Cash and marketable securities..................................    $   56,525     $   19,894
  Accounts receivable, net........................................       706,962        666,867
  Inventories less progress billings..............................       598,747        629,206
  Deferred tax assets.............................................       408,795        414,177
  Prepaid expenses................................................        30,390         30,272
                                                                      ----------     ----------
          Total Current Assets....................................     1,801,419      1,760,416
                                                                      ----------     ----------
Property, Plant and Equipment -- at cost..........................     1,567,511      1,559,636
  Less accumulated depreciation...................................      (926,668)      (905,091)
                                                                      ----------     ----------
Property, Plant and Equipment, Net................................       640,843        654,545
                                                                      ----------     ----------
Goodwill and Other Intangibles, Net...............................       727,374        737,554
                                                                      ----------     ----------
Other Assets and Long-term Investments............................       384,712        367,171
                                                                      ----------     ----------
          Total Assets............................................    $3,554,348     $3,519,686
                                                                      ==========     ==========
LIABILITIES AND SHAREHOLDERS' INVESTMENT
Current Liabilities
  Accounts payable................................................    $  816,373     $  869,880
  Payrolls and related expenses...................................       229,696        211,686
  Taxes on income.................................................       101,755         94,102
  Notes payable and current portion of long-term obligations......       160,029        147,182
  Contract liabilities and customer deposits......................       330,598        316,406
                                                                      ----------     ----------
          Total Current Liabilities...............................     1,638,451      1,639,256
                                                                      ----------     ----------
Long-term Obligations.............................................       494,133        507,344
                                                                      ----------     ----------
Postretirement Benefit Obligations Other than Pensions............       205,513        205,331
                                                                      ----------     ----------
Deferred Tax and Other Long-term Liabilities......................       131,032        128,736
                                                                      ----------     ----------
Shareholders' Investment
  Capital stock
     Voting preferred stock -- Series B...........................         2,053          2,053
     Common stock.................................................        46,075         45,996
  Additional paid-in capital......................................       305,522        301,839
  Retained earnings...............................................       770,919        730,019
  Cumulative currency translation adjustment......................       (39,350)       (40,888)
                                                                      ----------     ----------
          Total Shareholders' Investment..........................     1,085,219      1,039,019
                                                                      ----------     ----------
          Total Liabilities and Shareholders' Investment..........    $3,554,348     $3,519,686
                                                                      ==========     ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                        4
<PAGE>   5
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (THOUSANDS OF DOLLARS)
 
<TABLE>
<CAPTION>
                                                                           THREE MONTHS ENDED
                                                                               OCTOBER 31,
                                                                           -------------------
                                                                             1997       1996
                                                                           --------   --------
<S>                                                                        <C>        <C>
Cash and cash equivalents at beginning of period.........................  $  4,144   $ 77,105
                                                                           --------   --------
Cash was provided by (used for) operating activities
  Net earnings...........................................................    43,445     39,806
  Adjustments to reconcile net earnings to net cash provided by operating
     activities
     Depreciation and amortization.......................................    34,388     34,165
     Changes in assets and liabilities
       Accounts receivable...............................................   (37,949)    12,487
       Inventory.........................................................    30,003     (7,518)
       Prepaid expenses..................................................      (100)    (6,461)
       Accounts payable..................................................   (56,105)   (30,796)
       Payrolls and related expenses.....................................    17,263      5,703
       Deferred and current taxes on income..............................    14,645     20,493
       Contract liabilities and customer deposits........................    14,192     35,713
     Other operating activities..........................................    (3,382)    (9,782)
                                                                           --------   --------
Cash provided by operating activities....................................    56,400     93,810
                                                                           --------   --------
Investing activities
  Purchase of capital assets.............................................   (19,360)   (21,909)
  Other investing activities.............................................     3,291     13,507
                                                                           --------   --------
Cash used for investing activities.......................................   (16,069)    (8,402)
                                                                           --------   --------
Financing activities
  Change in short-term obligations, net..................................    (2,553)   (65,024)
  Other financing activities.............................................    (1,147)    (5,150)
                                                                           --------   --------
Cash used for financing activities.......................................    (3,700)   (70,174)
                                                                           --------   --------
Resulting in increase in cash and cash equivalents.......................    36,631     15,234
                                                                           --------   --------
Cash and cash equivalents at end of period...............................  $ 40,775   $ 92,339
                                                                           ========   ========
 
Supplemental disclosure of cash flow information
  Interest paid..........................................................  $ 17,569   $ 18,754
  Net income taxes paid..................................................  $  8,108   $  8,206
 
Reconciliation to Consolidated Balance Sheet at October 31, 1997:
  Cash and cash equivalents..............................................  $ 40,775
  Marketable securities..................................................    15,750
                                                                           --------
          Total cash and marketable securities...........................  $ 56,525
                                                                           ========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                        5
<PAGE>   6
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
 
                      THREE MONTHS ENDED OCTOBER 31, 1997
 
1. The amounts included in this report are unaudited; however, in the opinion of
   management, all adjustments necessary for a fair statement of results for the
   stated periods have been included. These adjustments are of a normal
   recurring nature. Certain information and footnote disclosures normally
   included in financial statements prepared in accordance with generally
   accepted accounting principles have been condensed or omitted. Certain
   reclassifications of prior period information were made for comparative
   purposes. These interim consolidated financial statements should be read in
   conjunction with the financial statements and notes thereto included in the
   Company's Annual Report to Shareholders for the fiscal year ended July 31,
   1997. The results of operations for the three months ended October 31, 1997
   are not necessarily indicative of operating results for the entire year.
 
2. The components of inventory balances are summarized below:
 
<TABLE>
<CAPTION>
                                                                  OCTOBER 31,      JULY 31,
                                                                     1997            1997
                                                                  -----------     ----------
                                                                    (THOUSANDS OF DOLLARS)
    <S>                                                           <C>             <C>
    Raw materials and work in progress........................    $   987,741     $  987,717
    Finished goods............................................         47,471         51,196
                                                                   ----------     ----------
                                                                    1,035,212      1,038,913
    Less progress billings....................................       (436,465)      (409,707)
                                                                   ----------     ----------
    Net inventories...........................................    $   598,747     $  629,206
                                                                   ==========     ==========
</TABLE>
 
3. Interest (expense) income is shown below:
 
<TABLE>
<CAPTION>
                                                                      THREE MONTHS ENDED
                                                                          OCTOBER 31,
                                                                     ---------------------
                                                                       1997         1996
                                                                     --------     --------
                                                                         (THOUSANDS OF
                                                                           DOLLARS)
    <S>                                                              <C>          <C>
    Interest expense.............................................    $(12,018)    $(13,636)
    Interest income..............................................       1,787        2,331
                                                                     --------     --------
    Net interest expense.........................................    $(10,231)    $(11,305)
                                                                     ========     ========
</TABLE>
 
4. On December 8, 1997, the Company announced that it has signed a definitive
   purchase agreement to acquire all of the issued and outstanding shares of
   capital stock of TASC, Inc. ("TASC") from Primark Corporation for
   approximately $432 million in cash. TASC provides information technology and
   services to government and commercial customers and, along with PRC Inc.,
   will help establish Litton as a major provider of information technology and
   system-based solutions for defense and non-defense related applications. This
   transaction, expected to be completed in April 1998, is subject to review by
   government regulatory agencies and approval by shareholders of Primark
   Corporation.
 
                                        6
<PAGE>   7
 
                   PART I. FINANCIAL INFORMATION (CONTINUED)
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS
 
     The Company reported sales of $1.04 billion for the first quarter ended
October 31, 1997, substantially comparable with the $1.05 billion for the first
quarter of fiscal year 1997. Operating profit for the first three months of
fiscal year 1998 increased to $96.0 million from the $91.6 million for the prior
year's first quarter. The higher operating profit and a reduction in interest
expense led to a 9% improvement in net earnings to $43.4 million, compared with
$39.8 million for the first three months of the prior year. Earnings per share
rose 11% to $.92 for the current quarter from $.83 for the first quarter of the
prior year.
 
     Effective August 1, 1997, the Company's Information Systems businesses are
reported as a separate business segment. Accordingly, the segment information
for the first quarter of fiscal year 1997 as discussed below has been restated
to reflect this change.
 
     Sales and operating profit for the Advanced Electronics segment were $413.3
million and $27.1 million, an increase from $370.7 million and $22.5 million,
respectively, for the first quarter of the prior year. These improvements
reflected increased volume and production rate on various programs in the
integrated avionics systems sector, as well as improved operating efficiency.
Backlog for the Advanced Electronics segment was $1.52 billion at the end of the
current quarter, compared with $1.61 billion at July 31, 1997. The Information
Systems segment reported sales of $252.9 million and operating profit of $17.4
million for the first quarter of fiscal year 1998 compared with $260.5 million
and $17.4 million, respectively, for the prior year's first quarter. The slight
decrease in sales was attributable to a slowdown in sales for the PRC Inc.
subsidiary's ("PRC") Super-Minicomputer program, which is an indefinite
delivery/indefinite quantity contract with various U.S. government agencies to
provide computer systems integration and networking solutions. During the first
quarter, PRC received important awards including a contract to provide
telecommunication and engineering segment services to the U.S. Navy, a
fixed-price, indefinite delivery/indefinite quantity contract to provide segment
hardware and software to the Military Health Service System within the
Department of Defense and an indefinite delivery/indefinite quantity contract to
provide software engineering and technical support for the Defense Logistics
Agency. These along with other awards increased PRC's unfunded backlog to $1.9
billion in potential contract values at October 31, 1997 from $1.5 billion at
July 31, 1997. Funded backlog for the Information Systems segment at October 31,
1997 was $502.7 million, compared with $518.1 million at July 31, 1997. As
discussed in Note 4 of Notes to Consolidated Financial Statements, subsequent to
the end of the first quarter, the Company announced that it has signed a
definitive purchase agreement to acquire TASC from Primark Corporation for
approximately $432 million in cash. As a provider of information technology and
services to both government and commercial customers, TASC will expand the
existing capabilities and business base of the Company's Information Systems
segment. This transaction, which is subject to review by government regulatory
agencies and approval by shareholders of Primark Corporation, is expected to be
completed in April 1998. The Marine Engineering and Production segment reported
sales of $238.6 million and operating profit of $30.1 million for the first
quarter of fiscal year 1998, compared with $299.2 million and $35.4 million,
respectively, for the prior year's first quarter. Sales at the Ingalls
Shipbuilding division were impacted by lower construction activity on contracts
nearing completion and contracts completed during fiscal year 1997, partially
offset by contracts moving into more advanced stages of production and the
startup on new contracts. Operating margin improved as a result of increased
earnings rates on programs maturing in the production process and continued cost
reduction efforts. Current construction activities include five Aegis
destroyers, two LHD class amphibious assault ships and six deepwater supply
vessels under a contract with a supplier of marine services to build 14 such
deepwater supply vessels. Backlog for this segment at October 31, 1997 was $3.09
billion, compared with $3.23 billion at July 31, 1997. Sales and operating
profit for the Electronic Components and Materials segment continued to benefit
from strong demand from the telecommunications industry for its commercial
electronic products. Operating margin for this segment also reflected continued
cost reduction efforts and process improvements.
 
     Net interest expense was $10.2 million in the first quarter of the current
fiscal year, a decrease over the $11.3 million for the prior year's first
quarter. The decrease was due to the net reduction in debt by more than $100
million during fiscal year 1997.
 
                                        7
<PAGE>   8
 
     Cash and marketable securities amounted to $56.5 million at October 31,
1997, compared with $19.9 million at fiscal year-end 1997. During the current
quarter, cash flow from operations provided the funds to meet operating needs,
make capital expenditures, and repurchase 57,500 shares of Common stock, leaving
approximately 2.9 million shares authorized to be repurchased. Management
believes that cash flow from operations, along with available credit
commitments, will be sufficient to meet operating requirements. In connection
with the previously mentioned acquisition of TASC, the Company expects to
generate the funds from available credit commitments, which amounted to $300
million at October 31, 1997, and from short to medium-term debt offerings
available under previously filed Form S-3 Registration Statements.
 
     Effective in the first quarter of fiscal year 1998, the Company adopted
Statement of Position 96-1 ("SOP 96-1"), "Environmental Remediation
Liabilities", issued by the American Institute of Certified Public Accountants.
The adoption of SOP 96-1 did not have an impact on the Company's results of
operations or financial position.
 
                           PART II. OTHER INFORMATION
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
(a) Exhibits
 
      Exhibit 3.1:  Amended and Restated By-laws of the Company as of October
                    16, 1997.
 
      Exhibit 3.2:  Amendment to Restated and Amended By-laws of the Company, as
                    adopted by the Board of Directors on December 4, 1997.
 
      Exhibit 10:   Litton Industries, Inc. Group Bonus Plan, as adopted by the
                    Company's Compensation and Selection Committee of the Board
                    of Directors on October 15, 1997.
 
      Exhibit 11:   Statement of Computation of Earnings per Share included
                    herein on page 9.
 
      Exhibit 27:   Financial Data Schedule.
 
(b) Reports on Form 8-K: There were no reports on Form 8-K filed during the
    first quarter ended October 31, 1997.
 
                                        8
<PAGE>   9
 
                                                                      EXHIBIT 11
 
                LITTON INDUSTRIES, INC. AND SUBSIDIARY COMPANIES
 
        PRIMARY EARNINGS PER SHARE AND FULLY DILUTED EARNINGS PER SHARE
                 (THOUSANDS OF DOLLARS, EXCEPT PER SHARE DATA)
 
<TABLE>
<CAPTION>
                                                                         THREE MONTHS ENDED
                                                                             OCTOBER 31,
                                                                      -------------------------
                                                                         1997          1996
                                                                      -----------   -----------
<S>                                                                   <C>           <C>
PRIMARY EARNINGS PER SHARE
  Earnings available for common shares and common stock equivalent
   shares deemed to have a dilutive effect:
     Earnings.......................................................  $    43,445   $    39,806
     Provision for cash dividends on preferred stock (Series B).....         (205)         (205)
                                                                      -----------   -----------
  Net earnings available for common shares and common stock
   equivalent shares deemed to have a dilutive effect...............  $    43,240   $    39,601
                                                                      ===========   ===========
  Primary earnings per share........................................  $      0.92   $      0.83
                                                                      ===========   ===========
 
FULLY DILUTED EARNINGS PER SHARE
  Net earnings available for common shares and common stock
   equivalent shares deemed to have a dilutive effect...............  $    43,240   $    39,601
                                                                      ===========   ===========
  Fully diluted earnings per share..................................  $      0.92   $      0.83
                                                                      ===========   ===========
 
Shares used in primary earnings per share computation
  Weighted average common shares outstanding (net of treasury
   shares)..........................................................   46,025,779    46,560,603
  Common stock equivalents..........................................    1,176,796     1,156,559
                                                                      -----------   -----------
  Total common shares and common stock equivalent shares deemed to
   have a dilutive effect...........................................   47,202,575    47,717,162
                                                                      ===========   ===========
Shares used in fully diluted earnings per share computation
  Total common shares and common stock equivalent shares deemed to
   have a dilutive effect...........................................   47,202,575    47,717,162
                                                                      ===========   ===========
</TABLE>
 
                                        9
<PAGE>   10
 
                                   SIGNATURE
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.
 
                                          LITTON INDUSTRIES, INC.
                                          (Registrant)
 
                                          By         /s/  Carol A. Wiesner
 
                                          --------------------------------------
                                                     Carol A. Wiesner
                                              Vice President and Controller
                                                (Chief Accounting Officer)
 
December 12, 1997
 
                                       10