What does greatest common multiple mean?

Answer 1

A multiple of a number x is xy where y is any integer. For example, multiples of 3 include 12 (3x4) 15 (3x5) and 36 (3x12)

A common multiple of x and z is any number that can be expressed as a multiple of x or z. For instance 36 is a common multiple of 3 and 4, as it is a multiple of both.

The term "greatest" means the highest valued number. For instance, the greatest out of 4, 68 and 20 is 68. It makes no sense to speak of a "greatest common multiple" as common multiples will go up to infinity. If I have a common multiple m, then 2m, 3m, 4m and so on will also be common multiples.