I was just thinking of the phrase “lowest common denominator” in the sense of something lowbrow that appeals to the unwashed masses, rather than something refined. And it occurred to me that in math, the lowest common denominator of a group of (natural) numbers is always going to be 1. What’s more interesting is the *largest* common denominator: it’s more interesting to know that 12 and 20 are both divisible by 4, than that they’re both divisible by 1.

Admittedly, I didn’t learn this part of arithmetic in the US (or even in English), so it’s possible that the phrase “lowest common denominator” is commonly understood to mean 1/*n*. In the example above, 1/4 is < 1/1, so 1/4 could be viewed as the lowest common denominator of 12 and 20.

But another possibility is that the phrase “lowest common denominator”, as applied to marketing and popular tastes, was originally ironic: a filmmaker might want to make a movie that appeals to the *largest* common denominator, i.e., one that’s as highbrow as possible, while still appealing to everyone. A critic who said that a movie appealed to the *lowest* common denominator would be saying that the movie appealed to the public’s basest tastes and wasn’t even trying to be good.

I haven’t found an etymological reference to confirm or disprove this, but I think it’s at least possible that the phrase started out ironic, but that over time people forgot this.