Let n be the least positive integer greater than 1000 for which

\operatorname{gcd}(63, n+120)=21 \quad \text { and } \quad \operatorname{gcd}(n+63,120)=60

What is the sum of the digits of n ?

**Answer Choices**

A. 12

B. 15

C. 18

D. 21

E. 24

Let n be the least positive integer greater than 1000 for which

\operatorname{gcd}(63, n+120)=21 \quad \text { and } \quad \operatorname{gcd}(n+63,120)=60

What is the sum of the digits of n ?

**Answer Choices**

A. 12

B. 15

C. 18

D. 21

E. 24