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 \dfrac{3}{4} of the probability of rolling a sum of 10 and the probability of rolling a sum of 12 is \dfrac{1}{12}. What is the least possible number of faces on the two dice combined?
Answer Choices
A. 16
B. 17
C. 18
D. 19
E. 20