The LA Business Journal in its current issue lists UCLA as the third-largest public employer in LA County with over 48,700 employees (and a budget of $7.7 billion) in 2018-19.
What about other universities? USC - which is a private employer and on a different list - is reported to have a little over 21,700 employees.
CalTech had just over 9,000. Cal State Northridge had a little over 4,100.