Possible Duplicate:
Is this GCD statement true?
Suppose we have integers $h$, $i$, $j$, and $k$. Can we always say that $ \gcd(h,i) \cdot \gcd(j,k) \,| \, \gcd(hj,ik) \ ?$ If so, how can we prove it?
Possible Duplicate:
Is this GCD statement true?
Suppose we have integers $h$, $i$, $j$, and $k$. Can we always say that $ \gcd(h,i) \cdot \gcd(j,k) \,| \, \gcd(hj,ik) \ ?$ If so, how can we prove it?