<p>The symbols (a,b,...,g) and [a,b,...,g] denote the greatest common divisor and lowest common multiple, respectively of the positive integers a,b,...,g. Prove that </p><p>                 [a,b,c]^2÷[a,b][a,c][b,c]=(a,b,c)^2÷(a,b)(a,c)(b,c)</p>