Why are we all assuming the OP is talking about Las Vegas in Nevada? Isn't the Las Vegas in New Mexico closer? But the route to there is pretty obvious - I25 south. Come to think of it, the I25/I40 route to Nevada goes through both Las Vegas.
Curiously Google Maps only gives one option, using US24 and CO9 to get to I70 as soon as possible. But what about staying with US24 all the way to I70, or US50 across the state to I70?
I have been thru them all and the trip north on I-25 to the western bypass then to I-70 is fast and save about 30 miles as opposed to going I-25 to I-70 directly. Going over the passes is pretty and very mountainous.
Las Vegas, NM is not assumed because unless a distinction is made, most assume Las Vegas, NV as the destination. May not be fair but when 40 million visitors come here each year, please forgive us for assuming as we do.
2011 Palomino Maverick 1000SLLB on a 2004 Dodge Quadcab CTD Ram3500 SRW long bed equipped with Timbren springs, Stable Load bump stops, Rickson 19.5" wheels/"G" range tires and a Helwig "Big Wig" rear anti sway bar.
Come on, what city has more historic buildings than a castle, a pyramid, the Eiffel tower, a Caesers palace, a Treasure Island, a Mirage, most of Manhattan? That and more all within about 3 miles and the admission is free. What you choose to invest is up to you. Enjoy the trip as either interstate route is wide and easy to follow.