AMC 10 2020a Problem 15

A positive integer divisor of $12!$ is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$? $\textbf{(A)}\ 3 \textbf{(B)}\ 5 \textbf{(C)}\ 12 \textbf{(D)}\ 18 \textbf{(E)}\ 23$