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Least Common Multiples and Greatest Common Factors

- Lesson 4.3

Least Common Multiple (LCM)

- The least common multiple is the smallest number

that is common between two lists of multiples.

EXAMPLE Find the LCM of 12 and 18

- The multiples of 12
- 12 x 1 12
- 12 x 2 24
- 12 x 3 36
- 12 x 4 48
- 12 x 5 60

- The multiples of 18
- 18 x 1 18
- 18 x 2 36
- 18 x 3 54
- 18 x 4 72
- 18 x 5 90

12, 24, 36, 48, 60

18, 36, 54, 72, 90

The first number you see in both lists is 36.

The least common multiple of 12 and 18 is 36.

Example 2 Find the LCM of 9 and 10

9, 18, 27, 36, 45, 54, 63, 72

81, 90, 99

10, 20, 30, 40, 50, 60, 70, 80

90, 100, 110

If you dont see a common multiple, make each

list go further.

The LCM of 9 and 10 is 90

Example 3Find the LCM of 4 and 12

4, 8, 12, 16

12, 24, 36

Answer 12

Example 4Find the LCM of 5 and 8

5, 10, 15, 20, 25, 30

35, 40

8, 16, 24, 32, 40, 48

Answer 40

Example 5Find the LCM of 6 and 20

6, 12, 18, 24, 30, 36

42, 48, 54, 60

20, 40, 60, 80, 100, 120

Answer 60

Greatest Common Factor (GCF)

- The greatest common factor is the largest factor

that two numbers share. - Lets find the GCF of 12 and 42. First, we need

to make a list of factors for each number.

12

42

1 x 12

1 x 42

Factors of 12 1, 2, 3, 4, 6,12

2 x 21

2 x 6

3 x 14

3 x 4

4 x ??

4 x 3

Factors of 42 1, 2, 3, 6, 7, 14, 21, 42

5 x ??

6 x 7

7 x 6

Common Factors 1, 2, 3, 6

Greatest Common Factor 6

What is the GCF of 18 and 27?

18

27

Factors of 18 1, 2, 3, 6, 9, 18

1 x 18

1 x 27

2 x ?

2 x 9

3 x 9

3 x 6

Factors of 27 1, 3, 9, 27

4 x ?

5 x ?

4 x ?

6 x ?

5 x ?

7 x ?

Common Factors 1, 3, 9

8 x ?

6 x 3

9 x 3

GCF 9

What is the GCF of 48 and 60?

Factors of 48 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

48

60

1 x 48

1 x 60

2 x 30

2 x 24

3 x 20

3 x 16

4 x 15

Factors of 60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20,

30, 60

4 x 12

5 x 12

6 x 8

6 x 10

Common Factors 1, 2, 3, 4, 6, 12

GCF 12

Homework Time

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