Isabel was right. Given two numbers, a and b, it is always verified the product
L.C.M(a,b) · H.C.F.(a,b)= a · b
The product of H.C.F and L.C.M. of two numbers is 9072. If one of the numbers is 72, we will find the other applying the result before. If we divide 9072 by 72 we obtain 126.
The question is why?. Because if we want to get L.C.M(a,b) we choose all the factors with the greatest exponent they appear and when we get H.C.F.(a,b) we choose the common factor with the smallest exponent they appear. Multiplying L.C.M(a,b) · H.C.F.(a,b) we find repeated factors but their product coincides perfectly with a · b where there are the same repeated factors and the factors corresponding to L.C.M(a,b) and H.C.F.(a,b). Check it with L.C.M(15,45) · H.C.F.(15,45) , for instance
Congratulations Isabel and Lydia! Thanks for your effort Javier. There will be extra points for everybody!