# Problem solving: Least common multiple

During a car race, two competitors will stop to fill up the fuel tank. One does it every 4 laps, and the other every 5 laps.

When the race begins, after how many laps will they meet at the fuel station, if they travel at the same speed?

Solution

The first competitor refill the tank every 4 laps

The first competitor will refill the tank after 4 laps, 8 laps, 12 laps, etc...

The situation is shown below

4, 8, 12, 16, 20, 24, 28, 32, 36

40, 44, 48, 52, 56, 60

The other competitor will refill the tank after 5 laps, 10 laps, 15 laps, etc...

The situation is shown below

5, 10, 15, 20, 25, 30, 35, 40

45, 50, 55, 60

The number in bold are what they have in common.

They will meet at the gas station after 20 laps, 40 laps, 60 laps, etc..

The least number they have in common is 20

We can also call this number the least common multiple.

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