A B737 CREW REPORTS MISSING HEARING THE RWY ASSIGNMENT ON THE LAX CIVET ARR. ATC PROVIDED VECTORS TO ASSIGNED RWY.

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ON APPROACH INTO LAX WE WERE HELD HIGH FOR TRAFFIC AND THEN GIVEN A CLEARANCE TO DESCENT VIA THE CIVET 4 AND MAINTAIN 250 KNOTS. NEITHER THE FO NOR I HEARD THE CLEARANCE TO DESCENT VIA THE CIVET 4 FOR RWY 25L. THE PM TRANSMITTED BACK DESCENT VIA THE CIVET 4 WITH NO RWY ASSIGNMENT. WE HAD PUT IN RWY 24R INTO THE FMS AND JUST PAST CIVET THE CONTROLLER STATED THAT WE WERE RIGHT OF COURSE AND ASKED WHICH RUNWAY FREQ WE HAD IN. WE STATED RWY 24R AND THE CONTROLLER STATED WE SHOULD BE ON RWY 25L; SO WE WERE GIVEN A HEADING OF 190 TO INTERCEPT THE RWY 25L COURSE. WE INTERCEPTED THE RWY 25L COURSE AND FLEW THE APPROACH WITHOUT ANY FURTHER PROBLEMS. UPON TAXIING IN WE WERE TOLD TO GIVE TRACON A CALL AT THE GATE. I CALLED TRACON AND TALKED WITH THE SUPERVISOR; HE HAD ALREADY LISTENED TO THE TAPES AND WE WERE GIVEN A RWY ASSIGNMENT WITH THE CIVET 4 CLEARANCE BUT WE DID NOT READ BACK THE RWY ASSIGNMENT. THERE WAS NO TRAFFIC CONFLICT AND HE STATED THAT THEY KNEW WHAT THE PROBLEM WAS RIGHT AWAY. CONFIRM CLEARANCES WITH THE OTHER PILOT. IF IN DOUBT; ASK AGAIN FOR THE CLEARANCE.