**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.

#### Example A

**5 and 3**

**Solution: 15**

#### Example B

**2 and 6**

**Solution: 6**

#### Example C

**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.

**Answer**

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.**

### Interactive Practice

### Video Review

Here are videos for review.

James Sousa Example of Determining Least Common Multiple Using a List of Multiples

- 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