CMO 2010 Problem 3

Three speed skaters have a friendly race on a skating oval. They all start from the same point and skate in the same direction, but with different speeds that they maintain throughout the race. The slowest skater does 1 lap a minute, the fastest one does 3.14 laps a minute, and the middle one does $L$ laps a minute for some $1<L<3.14$. The race ends at the moment when all three skaters again come together to the same point on the oval (which may differ from the starting