Find the greatest positive integer n for which n is divisible by all positive integers whose cube is not greater than n?

Answer 1

This statement is true only when n = 8
ie., 8 is divisible all positive integers below 8^(1/3) = 2 ===> 1 & 2.
if n >= 27 there are prime numbers in between which wont divide with n with 0 as remainder.