AHSME 1967 Problem 16

Let the product $(12)(15)(16)$, each factor written in base $b$, equals $3146$ in base $b$. Let $s=12+15+16$, each term expressed in base $b$. Then $s$, in base $b$, is $\textbf{(A)}\ 43 \textbf{(B)}\ 44 \textbf{(C)}\ 45 \textbf{(D)}\ 46 \textbf{(E)}\ 47$