1971 AHSME Problem 11

The numeral 47 in base a represents the same number as 74 in base b. Assuming that both bases are positive integers, the least possible value of a+b written as a Roman numeral, is

\textbf{(A) }\mathrm{XIII}\qquad \textbf{(B) }\mathrm{XV}\qquad \textbf{(C) }\mathrm{XXI}\qquad \textbf{(D) }\mathrm{XXIV}\qquad \textbf{(E) }\mathrm{XVI}

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