Actually, LAX-LAS Amtrak service existed at least until 1995 (I have a schedule and brochure from Amtrak from that year with the route in question). It seems to had been cancelled in 1996. A shame, too; more convenient than flying, a lot less weary than driving. Always did want to take that route but I was just 15 at the time.

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Best regards,
Dairenn Lombard
Los Angeles, CA