AMC 12 2022a Problem 4

The least common multiple of a positive integer $n$ and $18$ is $180$, and the greatest common divisor of $n$ and $45$ is $15$. What is the sum of the digits of $n$?

$\textbf{(A) } 3 \textbf{(B) } 6 \textbf{(C) } 8 \textbf{(D) } 9 \textbf{(E) } 12$