Question 20
given that $a, b, c$ are positive integers satisfying
$$
a+b+c=\operatorname{gcd}(a, b)+\operatorname{gcd}(b, c)+\operatorname{gcd}(c, a)+120
$$
determine the maximum possible value of $a$.
$$
a+b+c=\operatorname{gcd}(a, b)+\operatorname{gcd}(b, c)+\operatorname{gcd}(c, a)+120
$$
determine the maximum possible value of $a$.