Take any two coprime numbers and find their product. Also find out if the product of their HCF and LCM is equal to product of the numbers.

Hello!

Well, consider `a=12` and `b=25.` They are not prime but coprime (have no common dividers except `1` ). `a=2^2*3,` `b=5^2.`

Their product is `ab=12*25=300.` Their `HCF` is `1` as for any coprime numbers. Their `LCM` must include all their prime factors with their degrees, so `LCM=2^2*3*5^2=300.`

And yes,  `ab=HCF(a,b)*LCM(a,b)` for these `a` and `b.`

But wait, this identity is true for any natural `a` and `b` !  HCF is a factor of both `a` and `b,` so `a=a_1*HCF,` `b=b_1*HCF.` And because it is the highest common factor, the numbers `a_1` and `b_1` are coprime. Therefore LCM must include factors `HCF,` `a_1` and `b_1,` i.e. `LCM=HCF*a_1*b_1` and

`ab=a_1*b_1*HCF^2` and `LCM*HCF=a_1*b_1*HCF^2` also.