2016 AMC 10A Problem 5

A rectangular box has integer side lengths in the ratio 1: 3: 4. Which of the following could be the volume of the box?

\textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 144

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