AN MD80 CREW DEPARTED LAX ON THE RWY 24L LOOP 4 DEP WITH THE RWY 25R LOOP DEP IN THE FMS AND DEVIATED FROM THE SID ROUTING.

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ON THE LOOP 4 DEP FROM LAX; RWY 25R WAS SELECTED IN THE FMS INSTEAD OF RWY 24L; AND INCORRECT HDG WAS FLOWN FOR A SHORT TIME IN 'NAV' BTWN PASSING SMO 160 DEG RADIAL AND LATER RADIO HDGS FROM SOCAL DEP. NO IRREGULARITIES WERE MENTIONED BY DEP CTL. AFTER BEING UNACCUSTOMED TO TAKING OFF ON RWY 24L; AND VISUALLY NOTING THAT RWY 25R WAS BEING USED FOR DEPS; WE BRIEFED RWY 25R DEP BEFORE PUSHING OUT FROM OUR S COMPLEX LOCATION. IT WAS ALSO THE MORE TIME CONSTRAINED RWY OPTION. AFTER BEING ASSIGNED RWY 24L FROM GND CTL; WE FOCUSED ON THE DIFFERENT PWR AND FLAP SETTINGS FOR THE OTHER RWY (SHORTER RWY; AND WE HAD A RELATIVELY HIGH TKOF WT); AS WELL AS THE DIFFERENT TAXI RTE. NOTHING FLAGGED US TO CHANGE THE DEP RWY IN THE FMS; NOR TO PREPARE FOR THE DIFFERENT DEP HDGS. THIS WAS MY FAILURE AS CAPT TO REBRIEF THE DEP DURING TAXI OUT -- THE DEP NAME WAS THE SAME; BUT THE TKOF RWY WAS DIFFERENT; CHANGING THE DEP HDGS. IN THE FMS ACFT; THE SELECTED RWY WILL AUTOMATICALLY UPDATE THE IRS POS WHEN THE PWR IS ADVANCED; WHICH PLACED THE 'PURPLE LINE' EXACTLY WHERE WE WOULD HAVE EXPECTED IT TO BE ON THE HSI DISPLAY; THE IRS/FMS SYS BELIEVING THAT WE HAD ACTUALLY TAKEN OFF FROM RWY 25R. IN TRYING TO DETERMINE WHY WE HAD MADE THIS MISTAKE IN RETROSPECT; THERE HAS BEEN A LOT OF EMPHASIS AT THE AIRLINE ON 'RNAV' DEPS; AND MAKING SURE THAT THE CORRECT DEP RWY IS LOADED. HOWEVER; THIS BEING NOT AN RNAV DEP; WE RELAXED OUR GUARD. I DON'T KNOW WHY DEP CTL DIDN'T BRING THIS TO OUR ATTN AFTER XING THE SMO 160 DEG RADIAL BUT MY GUESS IS THAT WE HADN'T DEVIATED FAR ENOUGH FROM THE CORRECT DEP PATH TO GRAB THE CTLR'S ATTN; AND THERE WAS NO SIMULTANEOUS DEP FROM THE S COMPLEX. ON THE S COMPLEX; RWY 25R IS CURRENTLY DOING DOUBLE DUTY AS A LNDG AND TKOF RWY BECAUSE OF CLOSURE/CONSTRUCTION ON RWY 25L. THIS WAS ALSO EARLY MORNING; AND WE HAD A FORWARD ENTRY DOOR PROB AT DEP TIME. TO PREVENT THIS FROM HAPPENING AGAIN; I HAVE A SUGGESTION: SINCE MOST ALL PAX ACFT ARE NOW USING FMS; PERHAPS IT WOULD BE A GOOD IDEA TO PLACE INFO SIGNS IN STRATEGIC LOCATIONS REMINDING DEPARTING ACFT TO VERIFY THE DEP RWY IN THEIR CDU'S. THESE SIGNS COULD BE ADJACENT TO THE TXWYS CONNECTING THE N AND S COMPLEXES IN LAX; AS WELL AS TXWYS CONNECTING ARPT HALVES AT OTHER LOCATIONS WITH SIMILAR PARALLEL RWY ARRANGEMENTS (DFW; JFK; DEN; IAD; MIA; MSP; ETC).