Home > Pre-Algebra > Factors and Multiples > Least Common Multiple

## Least Common Multiple

#### Terms

Multiple - A number multiplied by any other whole number (like 1, 2, 3, 4 …)
Prime Number - A number that is evenly divisible only by itself or 1.

## Lesson

A Least Common Multiple (also known as LCM) is the lowest multiple of two or more numbers. A multiple of a number is that number multiplied by any other whole number (like a multiplication table!). So if we have to find the LCM of 4 and 6, we start by listing the multiples of both numbers from smallest to largest.

4: 4 (4x1), 8 (4x2), 12 (4x3), 16 (4x4), 20 (4x5), 24 (4x6), 28 (4x7)

6: 6 (6x1), 12 (6x2), 18 (6x3), 24 (6x4), 30 (6x5)…

Now we can see that the lowest number from both these lists is 12. Therefore, 12 is the LCM of 4 and 6.

Note: When all the numbers in the problem are prime numbers, it is quicker to determine the LCM by simply multiplying the numbers together.

If we have to find the LCM of 2, 3, and 5, we can simply do this:

$2 * 3 * 5 = 30$

## Examples

#### Least Common Multiple (Example #1)

$4\text{ and }5$
List the multiples of $4\text{ and }5$
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36
Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45
Find the least common multiple
LCM(4, 5) = 20

#### Least Common Multiple (Example #2)

$3\text{ and }12$
List the multiples of $3\text{ and }12$
Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27
Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108
Find the least common multiple
LCM(3, 12) = 12

#### Least Common Multiple (Example #3)

$3\text{ and }5$
List the multiples of $3\text{ and }5$
Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27
Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45
Find the least common multiple
LCM(3, 5) = 15

#### Least Common Multiple (Example #4)

$4, 6\text{ and }8$
List the multiples of $4, 6\text{ and }8$
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36
Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54
Multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72
Find the least common multiple
LCM(4, 6, 8) = 8