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 |