Question 29
Find all triples of positive integers $a$, $b$, $c$, such that
$$
a + (a, b) = b + (b, c) = c + (c, a),
$$
where by $(x, y)$ we denote the largest common divisor of integers $x$, $y$.
$$
a + (a, b) = b + (b, c) = c + (c, a),
$$
where by $(x, y)$ we denote the largest common divisor of integers $x$, $y$.