Can Mathematica execute the lcm and gcd functions in an equation? For instance, could it return a list of values for a, b, and c in the equation:

$\displaystyle (\text{lcm} (a,b))(\text{lcm} (b,c))(\text{lcm} (c,a))=(abc)\text{gcd} (a,b,c)$

Thanks in advance for the info!