2013 AMC 8 Problem 10

What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?

\textbf{(A)}\ 110 \qquad \textbf{(B)}\ 165 \qquad \textbf{(C)}\ 330 \qquad \textbf{(D)}\ 625 \qquad \textbf{(E)}\ 660

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