A PARTIAL FLAP APCH AND LNDG PERFORMED BY A B757 FLT CREW AFTER THEY RECEIVE A LEADING EDGE SLAT DISAGREE LIGHT DURING APCH TO LAS; NV.

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FLT TO LAS VEGAS (LAS) EXPERIENCED A SLAT PROB ON LNDG. AFTER DSNDING TO 8000 FT FOR APCH INTO LAS VEGAS; ATC SLOWED THE ACFT TO 210 KTS; THE FO CALLED FOR FLAPS 1 DEG. THE CAPT SELECTED FLAPS 1 DEG WITH THE FLAP HANDLE. MASTER CAUTION LIGHT ILLUMINATED ALONG WITH AN EICAS 'LEADING EDGE SLAT DISAGREE' MESSAGE. FLAP INDICATOR INDICATED BTWN UP AND 1 DEG ALONG WITH THE 'LEADING EDGE' CAUTION LIGHT ILLUMINATED. CAPT INFORMED ATC OF OUR PROB AND WE WERE INSTRUCTED TO HOLD PRESENT POS ON THE RWY 25L LOC AT 14 DME; 10 MI LEGS. FO (THE PF) SET UP THE HOLD WHILE THE CAPT GOT THE CHKLIST OUT. THE CAPT CONFIRMED THE PROPER CHKLIST WITH THE FO. DUTIES WERE THEN ASSIGNED: FO TO FLY THE PLANE AND TALK TO ATC; THE CAPT TO RUN THE CHKLIST. AFTER RUNNING THE 'LEADING EDGE SLAT DISAGREE' CHKLIST; ATC REQUESTED CLB TO 10000 FT. FO CLBED THE ACFT TO 10000 FT. THIS PUT THE PLANE IN AND OUT OF CLOUDS; SO ENG ANTI-ICE WAS SELECTED ON. WHILE THE CAPT WAS RUNNING THE 'LEADING EDGE SLAT ASYMMETRY' CHKLIST (LEADING EDGE SLAT DISAGREE CHKLIST TOOK US TO THIS CHKLIST); FO SENT ACARS MESSAGE TO DISPATCH TO CALL US. AFTER RUNNING THE CHKLIST TO ITS COMPLETION; THE CAPT TALKED TO DISPATCH; FLT ATTENDANTS AND THE PAX. FUEL AT THE START ON THE EMER WAS 8.7. AFTER BRIEFING APCH CONSIDERATIONS; RWY 25R WAS REQUESTED (14510 FT) AND EMER EQUIP TO BE STANDING BY. CAPT HAD PREPPED THE CABIN. NEXT; THERE WAS A CHANGE OF ACFT CTL. THE CAPT WAS THE PF NOW. FO SET UP RADIOS AND FMC FOR APCH TO RWY 25R. THE APCH WAS A VISUAL APCH WINDS CALM AND AUTOBRAKES #2 USED FOR LNDG. ALTERNATE TRAILING EDGE FLAPS 20 DEGS WITH A REF SPD 30 KTS MANEUVERING/REF +30 KTS FOR TARGET SPD USED. 160 KTS LNDG CARD WAS USED; FLAP 30 DEGS; MANEUVERING SPD OF 117 KTS +30 KTS FOR AN APCH SPD OF 147 KTS. FUEL WAS 7.0 AT THE START OF THE APCH. A BRACE SIGNAL WAS GIVEN AT 200 FT AGL AND A NORMAL LNDG WAS MADE. PAX WERE TOLD TO REMAIN IN THEIR SEATS. THE PLANE EXITED THE RWY AND HAD THE EMER TRUCKS CHK FOR HOT BRAKES BEFORE TAXIING INTO THE GATE. THE FOLLOWING FACTORS MADE THIS EMER RUN SMOOTHLY: LONG RWY (14510 FT); CALM WINDS; GOOD WX; ENOUGH FUEL TO HOLD AND RUN THE CHKLIST WITHOUT RUSHING; GOOD CREW COORD (COCKPIT AND CABIN); AND HELP FROM ATC. FO NEW ON ACFT 60 HRS IN TYPE. (JUST DID THIS CHKLIST IN TRAINING LESS THAN A MONTH AGO.)