Proving ab divides cd given divisibility conditions and gcd

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Homework Statement


Show that if a | c and b | c, and (a, b) = d, then ab | cd.

Homework Equations


The Attempt at a Solution


Abstract divisibility.
We have c=am, c=bn, and d=an+bm.
 

Discussion

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Could I multiply d=an+bm by c.
Then I have cd=acn+bcm
We have cd=c(an+bm)
cd=cd
Thus, ab | cd
 

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