Outbound flight on 13rd October from LGW with stop at Las Vegas for over 3 hours. Coming back to London Heathrow on 20th October.
I would go for the direct flight though, it's only 5£ more. Leaving from Heathrow on 13th arriving same day at 14:30. Return is on 20th , arriving ar Heathrow on 21st at 12:20 hours.