Given GCD of two numbers is 42 and their product is 15876. How many possible sets of members can be found? Given GCD of two numbers is 42 and their product is 15876. How many possible sets of numbers can be found? 
I have no idea. I can only evaluate the lcm. Don't know how to get the answers. 

Use $\gcd(x,y) \times \operatorname{lcm}(x,y) = xy$
\begin{array}{rrr}
                        xy &= &15876 \\
   \operatorname{lcm}(x,y) &=   &378 \\
\hline
                 \gcd(x,y) &=    &42
\end{array}
Assume $x < y$. Use $\gcd(p^a, p^b) = p^{min(a,b)}$ and 
$\operatorname{lcm}(p^a, p^b) = p^{max(a,b)}$ when $p$ is a prime number.
\begin{array}{rcr|ccc}
              \gcd(x,y) &=    &42 & 2^1 & 3^1 & 7^1 \\
\operatorname{lcm}(x,y) &=   &378 & 2^1 & 3^3 & 7^1 \\
                     xy &= &15876 & 2^2 & 3^4 & 7^2 \\
\hline
                      x &=    &42 & 2^1 & 3^1 & 7^1 \\
                      y &=   &378 & 2^1 & 3^3 & 7^1 \\
\end{array}
