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# Least Common Multiple

## Smallest number having the numbers as factors

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Least Common Multiple

Objective: To find the least common multiple (LCM) of a pair of numbers.

### Guidance

We can also find the least common multiple of a pair of numbers.

What is the least common multiple? The least common multiple (LCM) is just what it sounds like, the smallest multiple that two numbers have in common.

Let’s look back at the common multiples for 3 and 4.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

Here we know that the common multiples are 12, 24 and 36.

The LCM of these two numbers is 12. It is the smallest number that they both have in common.

We used lists of multiples for 3 and 4 to find the common multiples and then the least common multiple.

Find the Least Common Multiple for each pair of numbers.

5 and 3

Solution: 15

2 and 6

Solution: 6

4 and 6

Solution: 12

### Vocabulary

Here are the vocabulary words in this Concept.

Multiple
the product of a quantity and a whole number
Common Multiple
a number or numbers that two or more multiples have in common.
Least Common Multiple
a number that is the smallest multiple that two or more values have in common.

### Guided Practice

Here is one for you to try on your own.

Find the LCM of 20 and 15.

To do this, first let's list out the multiples of both numbers.

20 = 20, 40, 60, 80, 100

15 = 30, 45, 60

The LCM Of 20 and 15 is 60.

### Video Review

Here are videos for review.

1. http://www.mathplayground.com/howto_gcflcm.html – This video covers finding the greatest common factor and the least common multiple of two numbers.

### Practice

Directions: Find the least common multiple of each pair of numbers.

1. 3 and 5

2. 2 and 3

3. 3 and 4

4. 2 and 6

5. 3 and 9

6. 5 and 7

7. 4 and 12

8. 5 and 6

9. 10 and 12

10. 5 and 8

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