AMC 8 2017 Problem 12

The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers? $\textbf{(A) }2\text{ and }19 \textbf{(B) }20\text{ and }39 \textbf{(C) }40\text{ and }59 \textbf{(D) }60\text{ and }79 \textbf{(E) }80\text{ and }124$