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Home > Maths I > Relationships > Factors and multiples

Maths I

Factors and multiples

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Multiples

The multiples of a number are all the numbers that it will divide into. This includes the number itself.

  • For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16
  • The multiples of 5 are 5, 10, 15, 20, 25, 30, 35
  • The multiples of 20 are 20, 40, 60, 80, 15

Look at the lists - multiples are just like times tables.

Lowest 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 lowest number to appear in both lists, and it is called the lowest common multiple (LCM).

Question

What is the LCM of \;6 and \;10?

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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