What is the HCM of 108 and 180?

Answer 1

There can be no HCM (Highest Common Multiple). Suppose x is the HCM of two numbers a and b. That is to say, x is a multiple of a, x is a multiple of b and x is the highest such number.

Now consider the number 2x. It is a multiple of a, it is a multiple of b and it is greater than x. This contradicts the statement that x is the highest such number. So such an x cannot exist.