Question 4
Let $a$, $b$ and $c$ be natural numbers. Find the smallest value that the following expression can take:
$$
\frac{a}{\operatorname{gcd}(a+b, a-c)}+\frac{b}{\operatorname{gcd}(b+c, b-a)}+\frac{c}{\operatorname{gcd}(c+a, c-b)}
$$
$$
\frac{a}{\operatorname{gcd}(a+b, a-c)}+\frac{b}{\operatorname{gcd}(b+c, b-a)}+\frac{c}{\operatorname{gcd}(c+a, c-b)}
$$