Q: If J is the least positive integer that is divisible by every integer from 10 to 15 inclusive, then J/26 is =
Options:
(A) 1155
(B) 2310
(C) 4620
(D) 30030
(E) 60060 Let's give some random thoughts before answering.
The integer should be divisible by: 10, 11, 12, 13, 14 and 15, that is 5*2, 11, 3*2^2, 13, 2*7, and 3*5. The least common multiple of these integers is the product of 13, 11, 7, 5, 3 and 2^2. Then, R/26 is (13 * 11 * 7 * 5 * 3 * 2^2)/2 * 13 = 11*7*5*3*2 = 2310.
Therefore, the answer is (B).