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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?

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johnnymath
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    Your previous attempt included an answer to this very question. Back then it was homework; is it not homework any more? – Arturo Magidin Oct 17 '11 at 01:59
  • This problem is different. There is a small difference in each problem. In my previous question, I wanted to know if gcd(h,i)gcd(j,k)|gcd(hi,jk). Now I am just curious if gcd(h,i)gcd(j,k)|gcd(hj,ik). Notice the location of the $i$ and $j$ on the right hand side of each equation – johnnymath Oct 17 '11 at 02:41
  • Yes, but the second answer (Bill Dubuque's answer) you got there actually proved this problem. If the problem was incorrect then, the correct course of action would have been to edit that question to correct it, instead of posting it anew when this question was already answered there. If you did not understand Bill Dubuque's answer there, then you should ask for clarification through comments. I encourage you to edit that question to make the correction. – Arturo Magidin Oct 17 '11 at 02:43

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