Is it "a LLM" or "an LLM"?
More generally, do you choose the article as if the first letter of the initialism were pronounced or as if the first word of the initialism were pronounced? Does it differ with acronyms? Does it differ between the UK and America?
an, because the spoken sound of "LLM" starts with a vowel, "el". So, pronunciation of first letter of initialism, when you're spelling the initialism. I think.
Also [a history vs. an history][1].
[1]: https://www.reddit.com/r/grammar/comments/1ssrby/an_history_...
an LLM, an MP, an FBI agent, a CIA agent, a NASA engineer, an NSA mechanic, an 8 year old car, a 10 year old dog, et cetera – it's the sound of how you said those letters, always the sound.