Getting Lapped

Alice and Carla are swimming in a pool when they decide to have a race. Carla is pretty fast and swims at a rate of 81m/min, while Alice only swims at a rate of 64m/min. Both girls swim down and back multiple times, and because Carla is faster than Alice, Carla laps Alice a few times during the race. If \(t\) is the time it takes for Carla to lap Alice (in minutes) for the first time, what is the minimum length of the pool \(l\) such that \(l\) and \(t\) are positive integers?

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