Question 24
Let $n$ be the least positive integer greater than $1000$ for which $$
\begin{gathered} \gcd(63,n+120)=21\\ \text{and}\\ \gcd(n+63,120)=60. \end{gathered}
$$ What is the sum of the digits of $n?$
\begin{gathered} \gcd(63,n+120)=21\\ \text{and}\\ \gcd(n+63,120)=60. \end{gathered}
$$ What is the sum of the digits of $n?$