2020 Cayley Problem 12

The volume of a rectangular prism is 21. Its length, width and height are all different positive integers. The sum of its length, width and height is

\textbf{(A)}\ 11\quad \textbf{(B)}\ 13\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 9\quad \textbf{(E)}\ 17

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.