If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is =
Options:
(A) 5040
(B) 2520
(C) 1890
(D) 1260
(E) 630 OK. Let's think. Some random thoughts first:
The integer should be divisible by: 2, 3, 4, 5, 6, 7, 8 and 9, that is 2, 3, 2^2, 5, 2*3, 7, 2^3 and 3^2. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, L/2 is (7 * 5 * 3^2 * 2^3)/2 = 7*5*9*4 = 1260. The answer: (D).