There are a couple of Whistler digital scanners that are $233, so about $255 with tax if you have Prime, $264 with shipping if you do not have Prime. One is the WS1040 a handheld, the other a desktop WS1065.
They will do LAPD digital, but not many other agencies as more agencies are going to P25.
That is the best you can do I think as close to $200 and hear LAPD unless you go used.
Allen is right on the money about the radio he suggests. I like my Uniden P25 handheld the 325p2 as well, but it is just under $400 out the door.
Also that link for the 996P2 is a very good deal.
Good luck finding something you are happy with.