Lowest common denominator is a phrase with different meanings in different contexts. It means the LCD in maths (used for simplifying fractional arithmetic) and it also means the "basest form of something which all members of a population are able to comprehend/use".

There is a loose commonality in the usage but the term "lowest common denominator" as used here is not the mathematical term. GCF is a mathematical analogy but doesn't work as a direct usage as it would be unclear what the "factor" is that the people are to hold in common whilst in the original phrase it's clear that the denominator (standard) to be held in common is the sum of language understood [and used correctly] by all. It is lowest because greater ones can be achieved by excluding proportions of the population that has been used to establish the standard.

Whilst I couldn't care less the real meaning I've always assumed that "I could care less" is a shorthand for something along the lines of "I could care less but that's too much effort given how little I care about it". YMMV.

All language can be misunderstood by those who wish to misunderstand it.

E&OE.