Question 28
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 smallest common multiple of $x, y$.
$$
a + [a, b] = b + [b, c] = c + [c, a],
$$
where by $[x, y]$ we denote the smallest common multiple of $x, y$.