1967 AHSME Problem 16

Let the product (12)(15)(16), each factor written in base b, equal 3146 in base b. Let s=12+15+16, each term expressed in base b. Then s, in base b, is

\textbf{(A)}\ 43\qquad \textbf{(B)}\ 44\qquad \textbf{(C)}\ 45\qquad \textbf{(D)}\ 46\qquad \textbf{(E)}\ 47

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