Nod your head in a yes in case you were the type who did not like LCM and HCF in school. Nod your head again if you never or just rarely got correct answers in calculating LCM and HCF. Well, whatever ...

Suppose p is a prime integer. The LCM of (p^a, p^b) is p^{max(a, b)} If X = p1^a1 p2^a2 ... pn^an If we have to split their prime factors among a and b. We must give p1^a1 to at least one of (a, b).

It would take a long time to write out all the factors and multiples of 24 and 180 and compare the lists and it would be easy to make a mistake. A more efficient method is to use prime factors. Using ...