For simplicity, let us work only with positive integers.
We want to prove that if a,b,m are integers, then
First notice that any common multiple of and is also a multiple of , so any common multiple of and is of the form with some integer .
Now notice that if and , it cannot happen that and , since is the smallest number, So, when then , and if then . We conclude that is not a common multiple of and when .
So far, we proved that is a common multiple of and , and previous paragraph shows that there is no smaller common multiple, therefore is the least common multiple of and , in other words:
|Date of creation||2013-03-22 15:03:22|
|Last modified on||2013-03-22 15:03:22|
|Last modified by||drini (3)|