No. Prostitution is not legal in Las Vegas. Nevada is the only American state that allows it at all, but only inside licensed brothels in certain rural counties, and Clark County, which contains Las Vegas, is not one of them.
Why people think it is
Nevada’s reputation does most of the work. The state is the one place in the country with legal brothels, Las Vegas advertises adult entertainment on every corner, and escort cards and online ads are everywhere. None of that makes paying for sex lawful in the city. Strip clubs, adult shows and escort advertising are different things from the sex itself, and the law treats them differently.
Where it is legal in Nevada
State law lets counties with fewer than 700,000 residents license brothels, and a handful of rural counties do. The licensed brothels are a drive from Las Vegas, in places such as Pahrump in Nye County, and there are fewer than two dozen in the whole state. Clark County is too large to qualify, and other counties have chosen to ban them.
Inside a licensed brothel the work is regulated: workers are registered and tested, and the business is licensed. Outside one, selling or buying sex anywhere in Nevada is illegal.
Escorts in Las Vegas
Hiring company is not a crime. Paying for sex is. The usual arrangement in Las Vegas is an advertised escort whose fee is for time, with anything else a private matter, which is exactly the area police target in stings. Fake ads, robbery and payment scams are also common, and the people most at risk are visitors who do not know the city.
What the penalties are
Soliciting or engaging in prostitution outside a licensed brothel is a misdemeanour for a first offence in Nevada, and repeat offences carry heavier penalties. Any involvement of someone under 18, or of someone who is being coerced, is a serious felony.
How London compares
The position in England and Wales is close to the opposite of Nevada’s. Paying for sex between consenting adults is not a crime, but brothel keeping and soliciting in public are. If you are comparing, read the UK law guide, and if you are planning a trip, the visitor guide. The wider picture is in where prostitution is legal, country by country.