AMC 12 2015b Problem 23

A rectangular box measures $a \times b \times c$, where $a$, $b$, and $c$ are integers and $1\leq a \leq b \leq c$. The volume and the surface area of the box are numerically equal. How many ordered triples $(a,b,c)$ are possible?

\textbf{(A)} 4 \textbf{(B)} 10 \textbf{(C)} 12 \textbf{(D)} 21 \textbf{(E)} 26