2022 AMC 10A Problem 7

Prime factorize $18=2\cdot3^2,$ $45=3^2\cdot5,$ and $180=2^2\cdot3^2\cdot5.$ The lcm condition forces the exponent of $2$ in $n$ to be $2,$ the exponent of $5$ to be $1,$ the exponent of $3$ to be at most $2,$ and every other prime exponent to be $0.$ The gcd condition $\gcd(n,45)=15=3\cdot5$ further forces the exponent of $3$ in $n$ to be exactly $1.$ Therefore $n=2^2\cdot3\cdot5=60,$ and the sum of its digits is $6.$ Thus, B is the correct answer.