THE CREW OF AN A320 EXPERIENCED A DUAL FMGC FAILURE WHILE APCHING LAX ON THE CIVET 5.

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AFTER BEING CLRED DIRECT TO GRAMM INTXN BY ZLA; WE APPEARED TO LOSE AND THEN RECOVER BOTH FMGC'S. AFTER BEING HANDED OFF TO SOCAL (124.05) WE LOST THE FMGC'S A SECOND TIME; AND THEN RECOVERED THEM. WE ASKED FOR VECTORS TO THE ILS JUST IN CASE WE LOST THE FMGC'S AGAIN -- WHICH WE DID. WE WERE GIVEN A VECTOR TO INTERCEPT THE LAX 068 DEG RADIAL FOR THE ILS RWY 25L. DURING THIS TIME WE WERE TRYING TO DETERMINE THE EXACT NATURE OF OUR FAILURE (WE INITIALLY LOST BOTH AUTOPLTS; AUTOTHRUST; LNDG ELEVATION AND PARTIAL TUNING OF THE RADIOS). DURING THIS; SOCAL ASKED IF WE COULD TAKE A DIRECT TO SOMEWHERE AND INTERCEPT RWY 24R. WE REPLIED NO; THAT WE HAD LOST OUR MAIN NAV SYS AND HAD JUST SWITCHED TO OUR BACK-UP. THEY SOUNDED A BIT PERTURBED THAT WE REALLY WANTED TO STAY WITH RWY 25L; BUT THEY DID END UP LEAVING US ON THE APCH AND MOVING SOMEONE ELSE OVER TO RWY 24R. WE ELECTED NOT TO DECLARE AN EMER BECAUSE THE WX WAS WELL ABOVE WHAT WE NEEDED FOR A RAW DATA ILS AND WE HAD BEEN COMFORTABLY ESTABLISHED ON THE LOC. IN RETROSPECT; IT MIGHT HAVE JUT BEEN EASIER TO DECLARE AN EMER AND 'FORCE' THE ISSUE OF RWY ASSIGNMENT; BUT WE REALLY DIDN'T FEEL WE NEEDED TO BECAUSE SOCAL WAS VERY HELPFUL AND WE WERE TOTALLY COMFORTABLE WITH HOW THE SIT WAS PROGRESSING. UPON LNDG; MAINT DETERMINED IT WAS AN FMGC #1 FAILURE WITH NO REASON FOR FMGC #2 NOT ASSUMING THE NAV FUNCTIONS. SUPPLEMENTAL INFO FROM ACN 701206: AFTER WE EXPLAINED THAT IF WE DID NOT CONTINUE FOR MY RWY 25L THAT WE WOULD HAVE TO DECLARE AN EMER AND BREAK OFF THE APCH SOCAL WAS VERY HELPFUL FROM THAT POINT ON. THE REST OF THE APCH AND LNDG WAS UNEVENTFUL USING RAW DATA ON THE CAPT'S SIDE. UPON MAINT TROUBLESHOOTING; IT WAS CONFIRMED THAT FMGC #1 FAILED BUT NO EXPLANATION WHY FMGC #2 DID NOT BACK UP FMGC #1. UNIT WAS REPLACED AND CHKED OK. AFTER LNDG; I WAS GIVEN A PHONE NUMBER OF SOCAL TO CALL. AFTER EXPLAINING OF THE SIT TO SOCAL. THEY WERE VERY SYMPATHETIC TO OUR DILEMMA. IT WAS A BIT CONFUSING TO SOCAL DURING THE SIT AS WHY WE COULD NOT SWITCH RWYS. THERE WAS A MARINE LAYER MOVING IN AND WE COULD NOT SEE RWYS 24 FOR A VISUAL APCH.