2020 AMC 10A Problem 24

Let n be the least positive integer greater than 1000 for which\gcd(63, n+120) =21\quad \text{and} \quad \gcd(n+63, 120)=60.What is the sum of the digits of n?

\textbf{(A) } 12 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 18 \qquad\textbf{(D) } 21\qquad\textbf{(E) } 24

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