Positive integers, maths olympiad

Question

For each positive integer n, define S(n) to be the smallest positive integer divisible by each of the positive integers 1,2,3...,n. For example, S(5)=60. How many positive integers n are there such that 1≤n≤100 and S(n) = S(n+4)?

Answer 1

It sounds like n=n+4?