1998 Gauss 8 Problem 18

The figure shown is folded to form a cube. Three faces meet at each corner. If the numbers on the three faces at a corner are multiplied, what is the largest possible product?

\begin{array}{|c|c|c|}\hline \phantom{7} & 5 & \phantom{2} \\ \hline \phantom{7} & 6 & \phantom{2} \\ \hline 7 & 3 & 2 \\ \hline \phantom{7} & 8 & \phantom{2} \\ \hline \end{array}

\textbf{(A)}\ 144\quad \textbf{(B)}\ 168\quad \textbf{(C)}\ 240\quad \textbf{(D)}\ 280\quad \textbf{(E)}\ 336

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 Gauss contests here.