2012 AMC 8 Problem 15

The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?

\textbf{(A)}\ 40\text{ and }50\qquad\textbf{(B)}\ 51\text{ and }55\qquad\textbf{(C)}\ 56\text{ and }60\qquad\textbf{(D)}\ \text{61 and 65}\qquad\textbf{(E)}\ \text{66 and 99}

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