AMC 10 2020a Problem 24

Let $n$ be the least positive integer greater than $1000$ for which $$\gcd(63, n+120) =21 \text{and} \gcd(n+63, 120)=60.$$ What is the sum of the digits of $n$? $\textbf{(A) } 12 \textbf{(B) } 15 \textbf{(C) } 18 \textbf{(D) } 21 \textbf{(E) } 24$