Q: If R is the least positive integer that is divisible by every integer from 12 to 16 inclusive, then R/13 is =
Options:
(A) 40320
(B) 21840
(C) 1680
(D) 840
(E) 240 Let's give some random thoughts before answering.
The integer should be divisible by: 12, 13, 14, 15 and 16, that is 3*2^2, 13, 2*7, 3*5 and 2^4. The least common multiple of these integers is the product of 13, 7, 5, 3 and 2^4. Then, R/13 is (13 * 7 * 5 * 3 * 2^4)/13 = 7*5*3*16 = 1680.
Therefore, the answer is (C).