B737-800 CREW WAS ISSUED A GAR AFTER A COMMUTER ACFT DID NOT EXIT THE RWY AS EXPECTED.

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ON SHORT FINAL TO RWY 25L; TWR INSTRUCTED US TO GO AROUND DUE TO AN ACR Y ACFT THAT WAS STILL ROLLING OUT ON THE RWY. (THE ACFT DID NOT COMPLY WITH ATC INSTRUCTIONS TO EXIT THE RWY AT THE SPECIFIED TXWY.) WE COMPLIED WITH ATC INSTRUCTIONS AND WERE TOLD TO MAINTAIN RWY HDG AND 2000 FT. AFTER XING THE COASTLINE; WE WERE INSTRUCTED TO TURN L TO A HDG OF 220 DEGS; WHICH WE DID. A B747 THAT HAD TAKEN OFF OF RWY 25R ALSO TURNED TO THE SAME HDG; WHICH ATC OBSERVED AND STERNLY POINTED OUT THAT THE TURN WAS NOT FOR THEM AND GAVE THEM CORRECTIVE VECTORS NUMEROUS TIMES. APPARENTLY; THIS ENTIRE EVOLUTION LOOKED UNSAFE FROM THE GND ALTHOUGH WE DID NOT RECEIVE ANY TCASII ALERTS. WE WERE SUBSEQUENTLY VECTORED BACK FOR ANOTHER APCH AND LNDG WITH NO FURTHER INCIDENT. THE ACR Y ACFT THAT CAUSED THE GAR SEEMED TO HAVE USED UP AN EXCESSIVE AMOUNT OF RWY ON ROLLOUT. EXACTLY WHY IS UNKNOWN. THERE WERE 2 ACFT HOLDING SHORT OF RWY 25R AFTER HAVING CLRED RWY 25L; SO MAYBE HE DIDN'T WANT TO PULL UP BEHIND THEM FOR LACK OF ROOM OR JETBLAST CONSIDERATIONS. ANOTHER POSSIBILITY IS THAT THE CREW WANTED TO EXIT THE RWY ABEAM THEIR TERMINAL TO EXPEDITE TAXI. I WOULD STRONGLY RECOMMEND THAT ACR Y CREWS BE BRIEFED TO EXIT THE RWY AS SOON AS POSSIBLE AFTER LNDG; FOR OBVIOUS REASONS. SUPPLEMENTAL INFO FROM ACN 634800: WE WERE ON SHORT FINAL FOR RWY 25L AT LAX WHEN TWR ORDERED US TO GO AROUND BECAUSE OF A SAAB ON THE RWY ON ROLLOUT. WE EXECUTED THE GAR AND TWR SAID TO FLY RWY HDG AND CLB TO 2000 FT; TO WHICH WE COMPLIED. AT THE SAME TIME; AN ACR B747 JUST TOOK OFF FROM RWY 25R. TWR THEN DIRECTED US TO TURN L TO 220 DEGS. ACR TOOK THAT CALL AND BEGAN TURNING L TO 220 DEGS AS WE DID ALSO. TWR THEN REPEATEDLY ORDERED THE B747 TO TURN BACK TO RWY HDG. IN THE MEANTIME; WE WERE ACKNOWLEDGING OUR CALL OVER AND OVER TO MAKE SURE TWR KNEW WE WERE COMPLYING WITH HIS ORDER TO FLY 220 DEGS. WE NEVER SAW THE B747 UNTIL LATER WHEN HE WAS WELL OVER THE OCEAN AND WAS NO FACTOR. WE ALSO DON'T KNOW HOW CLOSE HE CAME TO US. WE FLEW AROUND FOR ANOTHER APCH TO RWY 25L AND LANDED WITHOUT FURTHER INCIDENT.