See below for explanation.
Let's say I was given a quadratic function that said:
Common multiples states we can keep the function exactly the same but simplify it a little so that the quadratic is easier to work with.
When you are factoring, it's sometimes simpler to reduce the function (or whatever you are given) so that it's easier to work with.
NOTE: The example I gave you, may NOT be factorable. Always follow up with examples from a creditable source.