One bicyclist can ride around a circular track in four minutes, a second in five minutes, and a third in six m?

60 minutes,

Multuply it out then find the least common factor.

The answer is indeed 60, but the wrong reason has been given. It is not always the least common multiple (LCM) of the times unless you require that the racers coincide at the starting point.

Suppose the first racer goes one once around in 4 minutes, the second in 1 1/3 minutes, and the third in 12/7 minutes. Well it's true that they will all coincide after 12 minutes, when the first has gone 3 laps, the second 9 laps and the third 7 laps. But it is also true that they will coincide after 6 minutes, when the first has gone 1.5 laps, the second 4.5 laps, and the third 3.5 laps.

Returning to the original problem, with rates 1/4, 1/5, and 1/6, the correct approach is to take the differences of the rates:

1/4 - 1/5 = 1/20

1/5 - 1/6 = 1/30

Now take the LCM of the 20 and the 30 and get 60 minutes. This will be the first time all three racers coincide.

In general, this may or may not be a time when they return to the starting point.

you need the LCD of the 3 numbers, 4,5,6.

that is 60. So they coincide in 60 minutes, after #1 has done 15 laps, #2 12 laps, and #3 10 laps.

.

60 minutes

60 minutes.

A long time LOL