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Maths

Factors and multiples

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Least common multiples (LCM)

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, …

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, …

The numbers 12, 24 and 36 appear in both lists, so they are known as common multiples.

The number 12 is the least number to appear in both lists, and it is called the least common multiple (LCM).

A lighthouse flashes every 6 seconds, another lighthouse signals every 10 seconds. They start by signalling together, when will they next flash at the same time?

Question

What is the LCM of 6 and 10?

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Answer

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42…

The multiples of 10 are 10, 20, 30, 40, 50…

The LCM of 6 and 10 is 30.

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