If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?

If \(\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}\), which of the following must be an integer?


I. \(\frac{x}{8}\)

II. \(\frac{x}{12}\)

III. \(\frac{x}{24}\)


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