\(X\) number of books have to be distributed equally among a number of library shelves. If \(X\) is a multiple of both

[Vincen]

\(X\) number of books have to be distributed equally among a number of library shelves. If \(X\) is a multiple of both \(9\) and \(6,\) which of the following statements must be true?

I. The books can be distributed equally among \(3\) library shelves.
II. The books can be distributed equally among \(27\) library shelves.
III. The books can be distributed equally among \(54\) library shelves.

A. I only
B. II only
C. III only
D. I, II, and III
E. None of the above

Answer: A

Source: e-GMAT