prove: if $ab\mid cd$ and $a\mid c$ and $ab\nmid c$ then $b\mid d$ [closed]

I'm having a hard time proving the following claim:

if $$ab\mid cd$$ and $$a\mid c$$ and $$ab\nmid c$$ then $$b\mid d$$

Any help would be appreciated

closed as off-topic by Eevee Trainer, Clayton, Vinyl_cape_jawa, Shaun, RRLMar 12 at 22:52

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• What have you tried so far? – Vinyl_cape_jawa Mar 12 at 20:26
• $ab\nmid c\,$ doesn't suffice, we need $(b,c/a)=1$ or equivalently $(ab,c)=a\$ – Bill Dubuque Mar 12 at 21:07

Counterexample: $$a=1,\,b=4,\,c=d=2$$.