Ask the city and you get a license count. Ask the county and you get a different license count. Add them together and you are wrong in both directions at once.
We pulled the records anyway. Every active business license file we could get from the City of Las Vegas and from Clark County came to 108,050 records. That number is real, and both governments publish the files, so you can go count them yourself. It is also not the answer to the question, for reasons that took us longer to accept than to discover.
First, a license is not a business. A restaurant with a bar holds a liquor license, a food license, and a general one, and that is one restaurant, not three companies. A single property management outfit can hold a dozen. So the raw count runs high.
Then it runs low. The valley is a patchwork of jurisdictions, and a shop in Henderson is licensed by Henderson, not by Clark County. If your pile only has city and county files, entire cities are simply absent from it. Ours was missing Henderson the first time we ran this, and the gap announced itself as a suspiciously clean hole in the map.
And the pile quietly overstates how alive it is. Licenses lapse mid-cycle, owners close up and never file anything, and the record keeps saying Licensed until the next renewal date embarrasses it.
So the honest answer to the question in the title is: it depends what you count, and anyone handing you one confident number without naming the records behind it is selling something.
Which is awkward to write, because we are also selling something. The bet we are making is on the citation. Every count we publish and every row we deliver names the government file it came from, so when a record is wrong, and public records are wrong more often than their formatting suggests, you can see exactly which office to argue with.
We will keep publishing what we count, as we count it.