Airport officials said at least 13 people were taken to hospital with minor injuries.
FAA spokesman Ian Gregor said the left engine of the Boeing 777-200 caught fire before take-off.
The plane was seen engulfed in flames and smoke. The fire was later put out.
The pilot later told passengers that the accident was the result of a “catastrophic failure of the engine”, reports the Guardian‘s Jacob Steinberg, who was onboard the plane.
Flight 2276 was bound for London’s Gatwick airport.
There were 159 passengers and 13 crew members on board.
The airport tweeted: “Received first call at 4:13 PM; flames were spotted at 4:14, and by 4:14 response was underway.”
It added: “@LASairport had the fire out and all passengers off BA flight by 4:18 PM – excellent work by our ARFF team.”
Airport officials said at least 13 people were taken to the city’s Sunrise hospital, most of them with injuries sustained while sliding down inflatable chutes during the evacuation.
Some of those on board said there was smoke in the cabin as one exit was opened and immediately declared unsafe.
An investigation into the blaze is now under way.
Officials later said one runway was shut down, but three others continued to operate.
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