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Bought a scooter new the other day - how often does a scooter need a MOT and a service by law?

MOT every year after the first three years (ie it doesn't need an MOT until it is three years old) and there is no legal requirement to ever have it serviced. With an LML its a pretty straight forward job to do it yourself, find a local scooter club and get them to go over it with you.
Anything that saves maybe £50 an hour of labour rates has to be worth learning.

THe service intervals are in your scooters paperwork if its new, but I'd recommend around 5,000km intervals to be on the safe side (around 3,000 miles), though IIRC its usually recomended to be around 7500km (5,000 miles).

No doubt someone will correct me, I'm not big on new machinery