AMC 12 2023b Problem 23

When $n$ standard six-sided dice are rolled, the product of the numbers rolled can be any of $936$ possible values. What is $n$?

\textbf{(A)}~11 \textbf{(B)}~6 \textbf{(C)}~8 \textbf{(D)}~10 \textbf{(E)}~9