2001 AMC 10 Problem 10

If x, y, and z are positive with xy = 24, xz = 48, and yz = 72, then x + y + z is

\textbf{(A) }18\qquad\textbf{(B) }19\qquad\textbf{(C) }20\qquad\textbf{(D) }22\qquad\textbf{(E) }24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.