Number Theory - If a|b and c|d, then ac|bd...

[Jamers328]

I have to prove that If a|b and c|d, then ac|bd.

So far I have:

Assume a|b and c|d. Then there are integers n and m with b=an, d=cm.
....
....
....
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Therefore ac|bd.



I know that at the end also bd=ac( ). But I don't know what goes in the ( ).

Any ideas?

Thank you in advance.

 

[stapel]

Hint: If b = an and d = cm, then what does bd equal?

Eliz.