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The multiples of a number are its products
with the natural numbers
1, 2, 3, 4, 5, ....
So, the multiples of 8 are 8, 16, 24, 32, and so on.
Note:
The multiples of a number are obtained by multiplying the number by each
of the natural numbers.
Example 13
Write down the first five multiples of 9.
Solution:
The multiples of 9 are obtained by multiplying 9 with the natural numbers
1, 2, 3, 4, 5 …
So, the first five multiples of 9 are 9, 18, 27, 36 and 45.
Common Multiples
Common multiples are multiples that are common to two or more
numbers.
E.g. Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18,
…
Multiples of 3 are 3, 6,
9, 12, 15, 18, …
So, common multiples of 2 and 3 are 6, 12, 18, …
Example 14
Find the common multiples of 3 and 4.
Solution:
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33,
36, …
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36,
…
So, the common multiples of 3 and 4 are 12, 24, 36, …
Lowest Common Multiple
The lowest common multiple (LCM) of two or more numbers is
the smallest common multiple.
E.g. Multiples of 8 are 8, 16, 24, 32, …
Multiples of 6 are 6, 12, 18, 24, …
In general:
To find the lowest common multiple (LCM) of two or more numbers, list the
multiples of the larger number and stop when you find a multiple of the
other number. This is the LCM.
Example 15
Find the lowest common multiple of 2 and 5.
Solution:
List the multiples of 5 and stop when you find a multiple of 2.
Multiples of 5 are 5, 10, …
Multiples of 2 are 2, 4, 6, 8, 10, …
Key Terms
multiples, natural numbers, common
multiples, lowest common multiple, LCM
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