2021 AMC 12B Problem 19

Two fair dice, each with at least 6 faces are rolled. On each face of each die is printed a distinct integer from 1 to the number of faces on that die, inclusive. The probability of rolling a sum of 7 is \frac34 of the probability of rolling a sum of 10, and the probability of rolling a sum of 12 is \frac{1}{12}. What is the least possible number of faces on the two dice combined?

\textbf{(A) }16 \qquad \textbf{(B) }17 \qquad \textbf{(C) }18\qquad \textbf{(D) }19 \qquad \textbf{(E) }20

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