MathNet 2019-part-04 — 184 problems (EN–VI) Question 108

Let $n$ be a positive integer. Determine the maximum value of $\operatorname{gcd}(a, b)+\operatorname{gcd}(b, c)+\operatorname{gcd}(c, a)$, under the condition that $a, b$ and $c$ are positive integers with $a+b+c=5 n$.