15=3×5 and its factors are 1, 3, 5 and 15. Its prime factors are 3 and 5, because 1 is not regarded as a prime number. 2 is the smallest prime and is not a factor of 15, but is a factor of 30.
30=2×3×5 and its factors are 1, 2, 3, 5, 6, 10, 15 and 30.
If ab is 30, then (a,b)=(1,30), (2,15), (3,10), (5,6).
The corresponding LCM(a,b)=30, 30, 30, 30.
The corresponding HCF(a,b) is 1, because only 1 divides into both factors. HCF is sometimes called GCF (greatest common factor).
The corresponding GCM(a,b), if GCM is greatest common multiple, is undefined but can be expressed as (correspondingly): 30n where n is a natural number (strictly positive integer) and n→∞. If GCM has the same meaning as GCF or HCF then GCM(a,b)=1.
Clearly none of the conditions can be met since ab=30 and LCM(a,b)=15 imply two contrary conditions: LCM(a,b)⇒(a,b)=(3,5) or (5,3); or (1,15) or (15,1) for all of which ab=15, not 30.
This question needs to be revised and/or rephrased.