http://newstudents.ucla.edu/studyarea/ says that the limit is 208 to 216 quarter units, depending on the division. Looks like 216 is most common, but check whichever division you transfer into. Note that 180 units is the minimum to complete a bachelor’s degree.
If you transfer with the minimum of 90 units, 216 units gives you 126 units before you reach the limit. Since a normal course load per quarter is 15 units, this is 8.4 quarters’ worth of normal course loads. If you transfer with the maximum of 105 units, you have 111 units, or 7.4 quarters of normal course loads.
Regarding financial aid, since it may come from varying sources and programs, the varying sources and programs may have different limits. It looks like the overall maximum limit is 150% of published length of program in terms of enrolled terms and units attempted (presumably including any terms that you received financial aid at your prior college), but some financial aid sources and programs have lower limits. See https://www.financialaid.ucla.edu/Portals/84/publications/2020-2021/FA_Handbook.pdf .