One bicyclist can ride around a circular track in four minutes, a second in five minutes, and a third in six minutes. If all three riders begin at the same time, how long will it be until they coincide the next time?

This classic puzzle isn't just a test of speed, but a problem of overlapping cycles. For all three riders to be at the starting line simultaneously, each one must have completed a whole number of laps. The first rider arrives back at the start every four minutes, the second every five, and the third every six. The goal is to find the very first point in time (Review) that is a multiple of all three of those numbers.

This mathematical concept is known as the Least Common Multiple (LCM). By looking at the multiples of each number (4, 8, 12...), (5, 10, 15...), and (6, 12, 18...), we can find the smallest number that appears in all three sequences. While they might pass each other elsewhere on the track, the first time they all meet back at the starting line is at the 60-minute mark. At this point, the first cyclist has completed 15 laps, the second has completed 12, and the third has completed 10.

This principle of finding a common cycle is used in many real-world applications, from scheduling recurring meetings to astronomy (Deals).