H.C.F & L.C.M. - Solved Examples

Q 1 - Compute H.C.F of (22* 23*5*74), (23*32*52*73) and (22*53*75).
A - 6760
B - 6860
C - 6960
D - 7060
Answer - B
Explanation
Prime numbers which are common to all the given numbers are 2,5 ,7.
∴ H.C.F = (22*5*73)= (4*5*343) = 6860

Q 2 - Find the H.C.F of 108, 360 and 600.
A - 12
B - 13
C - 14
D - 15
Answer - A
Explanation
108   = (22*33) , 360 = (23*32*5)  and 600 =  (23*52*3)
∴ H.C.F =  (22* 3) = (4* 3)=12

Q 3 - Find the H.C.F of 148 and 185.
A - 37
B - 38
C - 39
D - 40
Answer - A
Explanation
Remainder of 185/148 = 37
Remainder of 148/37 = 0
∴ H.C.F. = 37

Q 4 - Find the H.C.F of 204, 1190 and 1445.
A - 16
B - 17
C - 18
D - 19
Answer - B
Explanation
Remainder of 1190/204 = 170
Remainder of 204/170 = 34
Remainder of 170/34 = 0

∴ H.C.F. of 204, 1190 = 34

Remainder of 1145/34 = 17
Remainder of 34/17 = 0

∴ H.C.F. of 204, 1190 and 1145 = 17

Q 5 - Reduce 391/667 to lowest terms.
A - 7/29
B - 27/29
C - 17/29
D - 37/29
Answer - C
Explanation
First we find the H.C.F of 391 and 667.
Remainder of 667/391 = 276
Remainder of 391/276 =115
Remainder of 276/115 = 46
Remainder of 115/46 = 23
Remainder of 46/23= 0

∴ H.C.F. of 391, 667 = 23
∴    391/667   =( 391/23)/ (667/23)=  17/29

Q 6 - Find the L.C.M of (22*32*5*7) , (23*3*52*72) and (2*3*7*11).
A - 970200
B - 97020
C - 9702
D - 970
Answer - A
Explanation
We have  L.C.M = product of terms containing highest powers of (2,3,5,7,11)
= (23* 32* 52*72*11) = (8*9*25*11*49)= 970200

Q 7 - Find the L.C.M of 15, 18, 24, 27, 56.
A - 7260
B - 7360
C - 7460
D - 7560
Answer - D
Explanation
15 = 3 * 5
18 = 2* 3 * 3 = 2 * 3 2
24 = 2 *2 * 2 * 3   =  2 3 * 3
27 = 3 * 3 * 3 =  3 3
56 = 2 * 2 * 2 * 7=  2 3 * 7
L.C.M  = product of terms containing highest powers of (2,3,5,7) =2 3 * 3 3 * 5 * 7 = 7560

Q 8 - Find the H.C.F and L.C.M of 2/3 , 8/9  , 10/27  and 16/81.
A - 45 
B - 55 
C - 65 
D - 75 
Answer - D
Explanation
H.C.F of 2,8,10,16     = 2
L.C.M of  3,9,27,81 = 81                      
H.C.f =  H.C.F of 2,8,10,16/L.C.M of 3,9,27,81 = 2/81          
L.C.M =  L.C.M of 2,8,10,16/H.C.F of  3,9, 27,81 = 80/3

Q 9 - Two numbers are in the ratio 8:11 . Considering their H.C.f as 6, find the numbers.
A - 58.79
B - 48.66
C - 38.56
D - 28.33
Answer - B
Explanation
Let the numbers be 8x and 11 x. then, their H.C.F = x 
So, the numbers are (8*6), (11*6) i.e 48 and 66. 

Q 10 - Given the H.C. F of two numbers as 7 and their L.C.M as 210. If one of the numbers is 35, find the other. 
A - 32 
B - 42 
C - 52 
D - 62 
Answer - B
Explanation
Let the Other number be X. then, 
Product of numbers = product of their H.C .F and L.C.M
35*x=   7* 210  ⇒ x=  7*210/35  = 42
Hence, the other number is 42.

Q 11 - Three big drums contain 36 liters, 45 liters and 72 liters of oil. What is the biggest measure which can measure all the different quantities exactly?
A - 9 liters
B - 10 liters
C - 11 liters
D - 12 liters
Answer - A
Explanation
Required measure =   H.C.F  of 36 L, 45 L, and 72 L
= (32) liters = 9 liters
[As 36 = 22*32, 45 = 32*5 and 72 = 24* 34]

Q 12 - Four electronic devices make a beep after duration of 30 minutes, 1 hour, 3/2 hours and 1 hour 45 min. respectively. If all the devices beeped together at 12 noon at what time will they beep together again?
A - 9 am
B - 10 am 
C - 11 am
D - 11:30 am
Answer - A
Explanation
Intervals of beeping 30  min, 60 min, 90 min, 105 min.
Interval of beeping together= L.C.M of 30 min. 60 min. 90 min. 105 min
= (3*5*2*2*3*7) min. = 1260 min = 21 hrs.
So, they will beep together again next morning at 9 am.

Q 13 - Find the largest number which can exactly divide 513,  783 and 1107.
A - 22 
B - 23 
C - 24 
D - 25 
Answer - B
Explanation
Remainder of 783/513 = 270
Remainder of 513/270 =243
Remainder of 270/243 = 27
Remainder of 243/27 = 0

Remainder of 46/23= 0

∴ H.C.F. of 513, 783 = 23

Remainder of 1107/23 = 0

∴ H.C.F. of 513, 783 and 1107= 23

Q 14 - Find the smallest number which is exactly divisible by each one of the numbers 12, 15, 20 and 27.
A - 540
B -530
C - 520
D - 510
Answer - A
Explanation
Required no. = L.C.M of 12,15, 20 and 27
= (3*2*2*5*9) = 540

Q 15 - Find the least number which if divided by 6, 7, 8, 9, 12 leaves the same remainder 2 in each case.
A - 506 
B - 504 
C - 502 
D - 500 
Answer - A
Explanation
Required number =  (L.C.M  of 6,7,8,9,12)+2   =  (2*3*2*7*2*3)+ 2 = (504+2)= 506.

Q 16 - Find the largest natural number which can divide the product of any 4 consecutive natural numbers.
A - 23 
B - 24 
C - 25 
D - 26 
Answer - B
Explanation
(1*2*3*4) =  24
∴ Required number = 24

Q 17 - Find the least number which if divided by 35, 45  and 55 leaves the remainder 18, 28 and  38 respectively.
A - 3448  
B - 3458 
C - 3468 
D - 3478  
Answer - A
Explanation
Here (35-18) =  17 , (45-28)=  17  and (55- 38) =  17
Required number =  (L.C.M of 35,45, 55)- 17  = (3465 -17) = 3448

Q 18 - The H.C.F of 1/2 , 2/3 , 3/4 ,  4/5 is 
A - 1/120  
B - 12/5
C - 100/3
D - 10/3  
Answer - A
Explanation
H.C.F =   H.C.F of 1,2,3,4/ L.C.M  of  2,3,4,5   = 1/120                                                 

Q 19 - The H.C.F  of 2/3,  8/9 , 10/27  , 32/81.
A - 160/81
B - 160/3
C - 2/81
D - 2/3
Answer - C
Explanation
H.C.F  = H.C.F of 2, 8,10, 32/  L.C.M of 3,9, 27, 81   = 2/81

Q 20 - Which of the following is a pair of Co-primes?
A -  (14, 35) 
B - (18, 25) 
C - (31, 93) 
D - (32,62) 
Answer - B
Explanation
H.C.F of  18 and 25 is 1.
∴  18 and 25 are co-primes.


    87 Lectures 
     22.5 hours 

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