FLC OF A B757 LANDED ON THE WRONG PARALLEL RWY DUE TO A LACK OF CLR ATCT INSTRUCTIONS PRIOR TO LNDG.

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WE WERE RUNNING LATE ABOUT 40 MINS FROM DENVER TO LOS ANGELES. ZLA KEPT US HIGH AT CIVET FL220. WE WERE FILED FOR CIVET 4 ARR. WE WERE HANDED TO SOCAL APCH. APCH CTLR GAVE US DIFFERENT HDGS. FINALLY; WE WERE INSTRUCTED TO FOLLOW MITTS 1 ARR. SINCE WE WERE INSIDE MITTS; WE WERE GIVEN A HDG TO INTERCEPT LOC RWY 24R. WE REQUESTED APCH FOR S COMPLEX; WHICH WAS DENIED. HOWEVER; APCH CLRED US FOR VISUAL RWY 24L ALMOST 28 MI TOUCHDOWN. UPON CHANGING TO THE TWR FREQ; HE CLRED US TO LAND ON RWY 24R. ALTHOUGH; AFTER LISTENING TO THE TWR TAPES; MY FO HAD READ BACK THE INSTRUCTIONS AS 'CLRED TO LAND ON RWY 24R;' WE BOTH MISSED IT. AS WE TOUCHED DOWN ON RWY 24L; TWR INSTRUCTED US TO GO AROUND. IT WAS TOO LATE. WE WERE ALREADY STOPPING ON THE RWY WITH NO SEPARATION OR SAFETY COMPROMISED. MANY FACTORS CONTRIBUTED TO THIS EVENT: WE WERE HANDLED EXTREMELY POORLY. THE NUMBER OF THE TFC ON THE FINAL APCH SEEMED RATHER HIGH. WE WERE KEPT HIGH AND FAST DUE TO NUMEROUS XING TFC. APCH AND TWR FREQS WERE CLUTTERED. TWR DID NOT USE THE RIGHT PHRASEOLOGY TO SPECIFY THE RWY SWITCH. WE WERE LINED UP ON RWY 24L FOR 28 MI AND NOBODY (APCH OR TWR) SAID ANYTHING. I DID NOT UTILIZE MY JUMP SEAT RIDER AS PART MY CREW MEMBERS. HE WAS NOT WEARING A HEADSET. SUPPLEMENTAL INFO FROM ACN 422957: MANY FACTORS CONTRIBUTED TO THIS INCIDENT. THE CAPT AND MYSELF WERE BOTH TIRED. THIS WAS THE THIRD LEG OF THE FIFTH AND FINAL DAY OF OUR TRIP. WHEN WE LANDED IN LAX WE HAD BEEN ON DUTY FOR 13 HRS. BECAUSE OF FATIGUE; WE DID NOT CATCH THE RWY CHANGE TWR GAVE US. WE HAD BEEN LINED UP FOR RWY 24L FOR 25 MI. THIS WAS THE RWY WE WERE EXPECTING TO HEAR. ALSO; HAD THE CTL TWR USED THE PHRASEOLOGY 'SIDESTEP 24R' OR 'SWITCH TO 24R' WE PROBABLY WOULD HAVE HEARD THE RWY CHANGE. TWR CLRED 2 AIRPLANES TO CROSS RWY 24L WHEN WE WERE ON SHORT FINAL. WE DECIDED THESE ACFT WOULD CLR IN TIME; BUT THE SPACING WAS CLOSER THAN WHAT IS TYPICAL. FATIGUE AND SCHEDULING PRESSURES LED TO THE DECISION NOT TO GO AROUND; EVEN THOUGH IT DID NOT 'FEEL RIGHT.' HAD JUST ONE OF THESE CHAINS OF EVENTS BEEN BROKEN; THIS INCIDENT WOULD HAVE BEEN AVOIDED. I WILL MAKE AN EXTRA EFFORT TO NOT 'PAY LIP SVC' TO SOP CALLOUTS AND ATC READBACKS. BELOW 10000 FT; I WILL REQUEST JUMP SEAT RIDERS TO WEAR A HEADSET SO THEY CAN BE INCLUDED IN THE GOINGS ON.