Wikipedia has both forms: https://en.wikipedia.org/wiki/Lowest_common_denominator

I'm not a native speaker - this is a genuine question - does it sound weird to say "least common denominator"?

Native SAE-speaker here, studied linguistics in undergrad, and "least common denominator" is a perfectly normal construction.

The web isn't a perfect corpus, and Google isn't a perfect corpus analysis tool, but with those caveats...

Google results for "least common denominator": 738,000 / Google results for "most common denominator": 656,000

Additionally, as you point out, Wikipedia lists both as synonyms.

Your original comment was correct and idiomatic English.

A little. While I have heard it (from native speakers and non), it's less common. I also find it confusing because "least" can be interpreted as "lowest", or it can be interpreted in context of the following word: "common". "Least common" (meaning infrequent or most rare) changes the meaning to one different and misleading compared to "lowest", which is why I interpret this phrasing as sounding weird.

I think so? To me, least seems to be used for things like patience, distance, tidiness etc whereas lowest seems to be used more for money or countable things.