If \(x\) is the smallest positive integer that is divisible by each of the integers from \(24\) to \(27\) inclusive, whi

If \(x\) is the smallest positive integer that is divisible by each of the integers from \(24\) to \(27\) inclusive, which of the following statements must be true?

I) \(x>3200\)
II) \(x\) is a multiple of \(90\)
III) \(500\) is a factor of \(x\)

A) I only
B) II only
C) I and II
D) II and III
E) I, II, III

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT