If the numbers are 15a and 15b then 15(a+b)=15ab, where a and b have no factors in common, therefore a+b=ab and a=b/(b-1). If b=4, a=4/3 and the numbers are 15a=20 and 15b=60. If b=6, a=6/5 and the two numbers are 18 and 90. If a=b=2 both numbers are 30. But none of these pairs has an HCF of 15.