Question pertaining to the relationship between the GCD and LCM of 3 numbers.
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$