A B733 CREW RPTED THAT THEY LINED UP WITH THE WRONG RWY DURING APCH TO LAX.

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SMF-LAX. SADDE6 ARR. 7000 FT. ATC CLRS US 70 DEGS AFTER SMO FOR RWY 24R. WE REQUEST RWY 25L; BUT ARE TOLD UNABLE. ATC CLRS US TO DSND TO 2500 FT AFTER SMO. AFTER PASSING SMO AND BEGINNING DSCNT; ATC TELLS US TO STOP DSCNT AT 5000 FT -- WE WILL NOW GO TO RWY 25L. SEVERAL ACFT ARE POINTED OUT BY ATC. ACFT IS ON APCH TO RWY 24R; WE ARE GIVEN HDG 160 DEGS BEHIND THIS ACFT. 2 ADDITIONAL ACFT ARE POINTED OUT TO US ON APCH TO RWY 25L/25R. ON BASE FOR RWY 25L; WE ARE CLRED FOR RWY 25R APCH. (THIRD RWY IN LESS THAN 5 MINS.) AUTOPLT WAS USED DURING APCH TO AID IN TFC LOOKOUT. WHILE I WAS SEARCHING FOR PRECEDING TFC; FO (PNF) WAS 'HEADS DOWN' RELOADING THE BOX. ATC GAVE US HDG 220 DEGS TO JOIN LOC FOR RWY 25R. I SELECTED HDG 220 DEGS; THEN ARMED LOC. I WAS CONTINUING TO LOOK FOR/AVOID TFC. I NOTICED WE WERE OVERFLYING AN ACR AIRBUS ON FINAL ABOUT 1000 FT BELOW US. AT THIS TIME; ATC SAID 'CONFIRM YOU ARE LINED UP FOR RWY 25R.' I LOOKED UP; SAW WE HAD FLOWN THROUGH THE RWY 25R LOC; AND BEGAN CORRECTING BACK TO COURSE. I ALSO LOOKED DOWN AND NOTICED THAT RWY 25L WAS STILL 'IN THE BOX.' WE HAD NOT; AS I HAD THOUGHT; LOADED RWY 25R. CORRECTED BACK TO RWY 25R; WHILE MAINTAINING VISUAL WITH AIRBUS GOING TO RWY 25L. ATC TOLD US TO MAINTAIN HDG; MAINTAIN 2500 FT. FO READ BACK BOTH CLRNCS. I QUERIED HIM TO ASK IF WE WERE THEN CLRED FOR APCH. ATC THEN GAVE US L TURN; HDG 160 DEGS. SHORTLY AFTER; WE WERE CLRED TO MAINTAIN 3000 FT; AND FREQ CHANGE TO APCH. WE WERE THEN VECTORED AROUND FOR ILS RWY 25L; FULL STOP. HUMAN FACTORS/CLR: TASK SATURATION. MULTIPLE RWY ASSIGNMENTS IN BRIEF TIME PERIOD. WX: APCH INTO SETTING SUN; WITH TYPICALLY HAZY LAX WX. ATC: FREQ CONGESTION. SUPPLEMENTAL INFO FROM ACN 588740: PASSING ABOUT 5500 FT ABEAM THE FIELD; APCH ASKED IF DESIRED VISUAL TO RWY 25L. WE ACCEPTED. STOPPED DSCNT AT 5000 FT. TURNED BASE BEHIND ACR ON N COMPLEX. NOW CLRED VISUAL TO RWY 25R. S COMPLEX TFC ON TCASII. WE OVERSHOT RWY 25R. HAZE WITH SETTING SUN MADE FOR DIFFICULT SLANT RANGE VISIBILITY. ACR AIRBUS 1000 FT BELOW AND R OF US. WE LEVELED AT 2500 FT; CLEANED UP FOR GAR. APCH BROKE US OFF THE APCH. 160 DEG HDG; 3000 FT; VECTORS ILS; RWY 25L. FACTORS INCLUDED APCH TRYING TO DO US A FAVOR WITH THE S COMPLEX; WHICH WE ACCEPTED. WE DID NOT ANTICIPATE VISUAL TO 3 DIFFERENT RWYS WITHIN MINS (CHARTS OUT; ILS FREQS ON HAND; BOX LOADED).