AN ACR LGT CREW WITH AN ADVANCED COCKPIT HAD LTSS WITH ANOTHER ACFT IN THE LAX APCH CORRIDOR.

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WE HAD BEEN SET UP FOR AN ILS TO RWY 24 AT LAX. DURING MODIFIED BASE; WE WERE INSTRUCTED TO LAND ON RWY 24L (VISUAL). COPLT WAS FLYING AND I WAS REPROGRAMMING FMC FOR RWY 24L. WE WERE ALSO BEING GIVEN TFC TO FOLLOW FOR RWY 24L. WE THOUGHT WE HAD CORRECT TFC; SO WE BEGAN TURNING TO FINAL. I FINISHED PROGRAMMING FMC AND LOOKED UP TO SEE ANOTHER ACFT. NOW WE WERE UNSURE WHICH TFC TO FOLLOW. COPLT DECREASED BANK ANGLE UNTIL WE COULD FIGURE OUT THE TFC SIT. APCH ADVISED US WE WERE ENCROACHING ON RWY 25 APCH. HE GAVE US A TURN AWAY FROM THE RWY 25 APCH CORRIDOR BACK TO THE RWY 24L APCH. BY NOW WE REALIZED WE HAD BEEN WATCHING THE WRONG TFC. EVERY TIME I FLY INTO LAX; APCH CHANGES YOUR APCH OR LNDG RWY 1 TO 3 TIMES. WE HAVE TO REPROGRAM FMC EVERY TIME. ATC SHOULD REALIZE WITH AN AUTOMATED COCKPIT; APCH CHANGES DISTRACT ONE CREW MEMBER FROM TFC WATCHING. EVEN THOUGH THIS WAS SUPPOSED TO BE A VISUAL APCH; THE N SIDE OF COMPLEX WAS OBSCURED WITH A THIN CLOUD LAYER. THIS WAS WHY I WAS REPROGRAMMING THE FMC FOR RWY 24L.