In the mathematical - which those of a less relativist disposition would probably term "correct" - sense, the lowest common denominator of a collection of rational numbers expressed as fractions is the denominator of the largest unitary fraction in which they can all be expressed as integer multiples: in other words, the lowest common denominator of 1/4, 1/8 and 1/12 is 24 (not 1/24), because all of them can be expressed in integer multiples of 1/24 (and nothing larger): 6/24, 3/24 and 2/24.
The figurative usage of "lowest common denominator" has become commonplace, but has in fact zilch (0/24) to do with the mathematical meaning; indeed, in mathematical terms it comes conceptually closer to the highest common factor. As such, those who use it should be excoriated, eschewed, or at least considered as mathematical illiterates (bear this in mind when selecting people to take charge of large sums of money). However, this egregious cliché has probably become so firmly entrenched in the vocabularies of politicians and journalists1 that to struggle against it would be both quixotic and anathema to any reasonable descriptive linguist. Its meaning is somewhat difficult to fix, but the usage is undoubtedly pejorative (despite the fact that there seems to be nothing in the above example or any other that I can find that makes 24 a bad number) and is generally used to refer to cultural, social or occasionally political phenomena which are designed (generally for financial motives) to appeal to or cater for a large number of people, excluding the speaker (and generally to those the speaker considers to be of a lower social or intellectual standing, albeit probably including their teenage children); in other words, it is more or less a derogatory synonym for majority taste, that which satisfies the largest number of people. This is presumably because both "low" and "common" have negative connotations, while "denominator" just completes the collocation without anybody being particularly concerned about whether it means anything.
- Don't get me wrong; mostly I quite like politicians and journalists, or at least I don't consider their existence as inherently evil, except when they get sloppy. Can't abide sloppy usage, though, at least in others.