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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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    Your [previous attempt](http://math.stackexchange.com/questions/72523/is-this-gcd-statement-true) included an answer to this very question. Back then it was homework; is it not homework any more?2011-10-17
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    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 equation2011-10-17
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    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.2011-10-17

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