This refers to the smallest positive number that is a multiple of two or more numbers.
Let’s begin with an example. Find the least common multiple of 3 and 5?
SOLUTION
The multiples of 3 are 3, 6, 9, 12, 15 and so on
The multiples of 5 on the other hand are 5, 10, 15, 20, 25 and so on.
MULTIPLE
The multiple of a number is gotten when we multiply it by another number. It is just like multiplying it by 1, 2, 3, 4 and so on but not zero. Below are some examples:
COMMON MULTIPLE
Common multiples are those numbers that appear in both the numbers that you have listed. For example, if you list the multiples of 4 and 6,
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36 and so on
Multiples of 6 are 6, 12, 18, 24, 30, 36 and so on
Note that 12 and 36 appear in both the lists. Therefore, 12 and 36 are common multiples of 4 and 6.
LEAST COMMON MULTIPLE
This refers to the smallest of the common multiples. In the example above, the least common multiple of 4 and 6 is 12.
Find the least common multiple of 4 and 10. Again, you start by listing the multiples of both the numbers.
Multiples of 4 are: 4, 8, 12, 16, 20, 24 and so on
Multiples of 10 are: 10, 20, 30 ,40 and so on
The multiple that is common in both the listings is 20. This makes it the least common multiple of 4 and 10.
Find the least common multiple of 4, 6 and 8.
Multiples of 4 are 4, 8, 12, 16, 20, 24 and so on
Multiples of 6 are 6, 12, 18, 24, 30 and so on
Multiples of 8 are 8, 16, 24, 32, 40 and so on
Therefore, 24 is the least common multiple of 4, 6 and 8 because there is no lesser number in all the three listings.
