How can factors find a common denominator?

Factors can help find a common denominator because it allows you to see what numbers are shared between your two denominators.

For instance, 4 is a factor of 12.

So, if you have one denominator of 4, and one of 12, you have an official bruh moment and you can see that to get your common denominator, all ya gotta do is multiply the fraction with a denominator of 4 by 3/3

4a^-2b^3c^-4d=4b^3d/a^2c^4