With the help of Wikipedia, I counted all of the official exit numbers of Los Angeles County, and there are 635 of them. *WHEW* Of course if you were to include Greater Los Angeles (LA, Orange, Ventura, San Bernardino and Riverside Counties), there'd be a lot more.
I went through each freeway and freeway portion within Los Angeles County. Included are exits to other freeways (transition roads), not just exits to a surface street.
The breakdown:

CA-2 - 18 exits

I-5- 84 exits

I-10 - 66 exits

CA-14 - 30 exits

CA-22 - 1 exit

CA-47- 5 exits

CA-57- 14 exits

CA-60 - 35 exits

CA-71 - 6 exits

CA-90 - 2 exits

CA-91 - 23 exits

US-101 - 63 exits

CA-103 - 2 exits

I-105 - 17 exits

/

I-110/CA-110 - 50 exits

CA-118 - 15 exits

CA-126 - 1 exit

CA-134 - 20 exits

CA-170 - 10 exits

/

I-210/CA-210 - 53 exits

I-405 - 61 exits

I-605 - 29 exits

I-710 - 30 exits