B737 FLT CREW OVERSHOOTS RWY 24R ON APCH TO LAX.

Narrative

INBOUND TO LAX WE WERE PRECEDED BY A HEAVY 747. WE ENCOUNTERED TURBULENCE/WAKE SEVERAL TIMES FROM N OF SMO VORTAC. APCH ASKED IF WE COULD TURN IN AT THE MARKER AND WE SAID WE COULD WHICH WOULD PUT US INSIDE OF THE 747. THE FO DID A VERY GOOD JOB OF CONFIGURING THE PLANE AND WAS STABLE AND ON A PROPER INTERCEPT TO THE LOC. AFTER THE HANDOFF TO TWR THE FREQ WAS BUSY. I DECIDED TO CHECK THE TCAS DISPLAY TO SEE HOW CLOSE THE FOLLOWING 747 WAS. AS I CHECKED THE TCAS LAX TWR ASKED IF WE WERE CORRECTING OUR COURSE. I REALIZED THAT WE HAD NOT TURNED IN AND WERE STARTING TO ENCROACH ON THE S SIDE APCH AIRSPACE. WHILE WE WERE MORE THAN 2 HRS DELAYED DUE TO SINGLE RWY LNDG OPS AT ZZZ THE DELAY WAS NOT A FACTOR. I SHOULD HAVE DONE A BETTER JOB OF PRIORITIZING MY MONITORING PRIORITIES. INTERCEPTING THE LOCALIZER WAS FAR MORE IMPORTANT THAN THE SPACING OF AN ACFT IN TRAIL. IN RETROSPECT; I ALSO THINK I WILL AND WILL ENCOURAGE OTHER PLTS TO USE THE CWS MODE OF THE AUTOPLT WITH THE LOC (AT MINIMUM) OR APCH MODE ARMED INSTEAD OF HAND FLYING. THIS WILL HELP TO ENSURE THE INTERCEPT AND TO ESTABLISH THE PROPER INITIAL GROUND TRACK. ONCE ESTABLISHED INBOUND; HAND FLYING WITH THE AUTOPLT OFF WOULD BE OK. A GREAT JOB BY LAX TOWER ON THE HEADS UP ALSO.