Question 122
Find out how many solutions the equation
$$
[a^2, b^2] + [b^2, c^2] + [c^2, a^2] = (a^2, b^2)(b^2, c^2)(c^2, a^2)
$$
can have in natural numbers, where $[m, n]$ and $(m, n)$ denote respectively the LCM and the GCD of the natural numbers $m$ and $n$.
$$
[a^2, b^2] + [b^2, c^2] + [c^2, a^2] = (a^2, b^2)(b^2, c^2)(c^2, a^2)
$$
can have in natural numbers, where $[m, n]$ and $(m, n)$ denote respectively the LCM and the GCD of the natural numbers $m$ and $n$.