2021 Fall AMC 12A Problem 8

Let M be the least common multiple of all the integers 10 through 30, inclusive. Let N be the least common multiple of M,32,33,34,35,36,37,38,39, and 40. What is the value of \frac{N}{M}?

\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 37 \qquad\textbf{(D)}\ 74 \qquad\textbf{(E)}\ 2886

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