What is the difference between the two smallest integers?

Question

There is more than one integer greater than 1 which, when divided by any integer k such that 2 ≤ k ≤ 11, it will have a remainder of 1.

So far, the only answer is not correct.

Answer 1

All integers, which when divided by by any integer k such that 2 ≤ k ≤ 11 have a remainder of 1, are of the form:

n*lcm(2,3,...,11) + 1 for all integers n. Thus the difference between the smallest two is:

lcm(2,3,...,11) =
8*9*5*7*11 =
27720

Answer 2

Well, the smallest number would be 3 because 2/3 gives you 1 r1 and the second smallest would be 4 because 4/3 gives you 1 r1 also.

So 4 - 3 = 1