ZLA CLRS GLF4 DIRECT LAS VORTAC ON COURSE; BUT FO SELECTS LVS VORTAC RESULTING IN A COURSE DEV. CAPT QUESTIONS NAVAID NAME COMMONALITY.

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DEP POINT -- SMO (SANTA MONICA): ON CLBOUT; WE WERE GIVEN SEVERAL RE-RTES (CHANGES) WHICH PUT US MORE DIRECT TO DEST (GJT). OUR FINAL CHANGE FROM ZLA WAS DIRECT LAS VEGAS; NV; DIRECT HVE DIRECT DEST. THE INSTRUCTION FROM THE CTLR WAS GIVEN TO US USING FULL NAME OF THE FIX; THEN THE IDENTIFIER FOR HVE; DIRECT DEST. THE CTLR DID SAY LAS VEGAS; NV; BUT WHEN MY COPLT LOOKED UP THE IDENTIFIER FOR LAS VEGAS; NV (IN THE 'ACCU' QUICK NAVAID SECTION); HE MISTAKENLY USED LAS VEGAS; NM; INSTEAD. THAT GAVE US APPROX 35 DEGS OF DIVERGENT COURSE -- WHICH WE DID NOT CATCH. CTR ASKED IF WE WERE GOING DIRECT LAS VEGAS. MY COPLT RESPONDED SAYING; 'WE WERE DIRECT LVS.' AT THAT POINT THE CTLR CORRECTED OUR DIRECT TO AND THE REST OF THE FLT WAS UNEVENTFUL. WE WERE GIVEN A HDG (010 DEGS) TO FLY FOR A BRIEF TIME AND THEN RECLRED TO LAS. SHORTLY AFTERWARD; I CALLED ZLA ON THE FLT PHONE TO CONFIRM THAT THERE WERE NO ISSUES OR PROBS WITH OUR ERROR. WE WERE TOLD THAT THERE WAS NO PROB AND EVERYTHING WAS FINE. RECOMMEND THAT IN THE FUTURE; WHEN THERE ARE MULTIPLE LOCATIONS WITH THE SAME NAME; THE IDENTIFIER BE USED RATHER THAN THE FULL NAME. THE CTLR USED THE IDENTIFIER FOR THE SECOND POINT; WHY NOT THE FIRST POINT WHICH WAS MUCH EASIER TO MISTAKE?