How do you Find a pair of numbers whose LCM is 75 and whose GCF is 5?

75 = 3*5*5, so the first pair that comes to mind is 3*5 and 5*5.

LCM(15, 25) = 75.

And it conveniently happens to be that GCD*(15, 25) = 5.

So {15, 25} is the answer (at least an answer).

*GCD is "Greatest Common Divisor" and a more official way of saying GCF.

* * * * *

Yes, it is an answer.

Consider LCM/GCF = 75/5 = 15

If p and q are any two coprime factors of LCM/GCF = 15, then p*GCF and q*GCF will be an answer.

The above answer used p = 3 and q = 5.

The other possible pair is p = 1 and q = 15 which gives the pair as 5 and 75.