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So set your monitor to 119.88 instead of 120.

Theres a reason why monitors give you both x/1000 and x/1001 framerates.

I didn't know this was possible, but in such a case why not set a 60Hz display to 48Hz, 59.95Hz, etc.?

48hz is supported on few monitors, not often (but can be hit by gsync/freesync/VRR); 24hz is sometimes supported (often seen in TVs).

And you can set it to 59.94, nobody is stopping you.

This entire comment chain started with, essentially, what is the LCM of 60 and 24 (or 59.94 and 23.976), and its 120 (or 119.88).