Find all triples of positive integers $(x, y, z)$ satisfying $x < y < z$, $gcd(x, y) = 6, gcd(y, z) = 10, gcd(z, x) = 8$ and $lcm(x, y,z) = 2400$.
Problem
Source: 2004 Estonia National Olympiad Final Round grade 10 p1
Tags: GCD, LCM, number theory
Source: 2004 Estonia National Olympiad Final Round grade 10 p1
Tags: GCD, LCM, number theory
Find all triples of positive integers $(x, y, z)$ satisfying $x < y < z$, $gcd(x, y) = 6, gcd(y, z) = 10, gcd(z, x) = 8$ and $lcm(x, y,z) = 2400$.