A B737-700 Captain reported encountering wake turbulence from a preceding B747 on a parallel runway at LAX.

Narrative

We were approximately 25 miles out for 24R [at LAX] when ATC crossed a B747 at ten miles for 24L. The surface winds were a crosswind from right to left; but the winds at altitude were left to right; which must have kept the B747's jet wash lingering in our approach path. I flew slightly high; but still encountered the turbulence at about 15 miles at about 4;500 FT. I believe we were at flaps 5 slowing to 170 KTS per ATC. We rolled abruptly to the left; but only about 20 degrees before the autopilot was disengaged. The remainder of the approach was flown by hand; slightly steep (1/2 dot or so) until about 1;000 FT AGL. As we were below 10;000 FT in a sterile cockpit; I did not make a PA. We landed without incident and turned off at the reverse and immediately crossed 24L per the Tower. The taxi was short and very congested and; again; I did not stop the aircraft to make a PA. Once safely parked at our gate; I made myself available at the front of the aircraft to answer customer questions. There were a few; but no one seemed overly agitated or alarmed. [It's] nearly impossible to consistently predict where jet wash will be encountered; even if protective measures are taken; as we did. Next time; I may elect to go-around. This is the first time SoCal Approach has placed a B747 across my final at LAX (probably with good intentions on their part).