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There are infinitely many such pairs.

For example,

suppose p, q, r and s are 4 prime numbers.

Then p*q and r*s are both composite but p*q and r*s are coprime.

And you could always mutiply either one of them by the prime number t, and maybe the other one by another r to give p*q*t and r2*s. And so on.

So, for example 2*7 = 14

and 3*5 = 15 form such a pair.

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Q: What are 2 composite numbers that are relatively prime?
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