1965 AHSME Problem 33

If the number 15!, that is, 15 \cdot 14 \cdot 13 \ldots 1, ends with k zeros when given to the base 12 and ends with h zeros when given to the base 10, then k + h equals:

\textbf{(A)}\ 5 \qquad \textbf{(B) }\ 6 \qquad \textbf{(C) }\ 7 \qquad \textbf{(D) }\ 8 \qquad \textbf{(E) }\ 9

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