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5.4 Least Common Multiple

Finding a Common Multiple

A multiple shared by 2 or more numbers is called

a common multiple.

Examples of multiples

2

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24,

5

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,

8

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, .

Finding a Common Multiple Continued

To find a common multiple between 2 or more

numbers, you can choose between 2 methods.

Method 1 Listing Multiples

Step 1 List multiples of each number.

2

2, 4, 6, 8, 10

Step 2 Circle the smallest common number in

both set of multiples.

3

3, 6, 9, 12, 15, 18

LCM 6

Tip If you multiply the 2 numbers together,

that number is how far you need to list each

multiple out to.

6

6, 12, 18, 24, 30, 36

18

18, 36, 54

LCM 18

Finding a Common Multiple Continued

Method 2 Prime Factorization (Factor Trees)

2

3

Because 2 and 3 are both prime numbers, simply

multiply them together. LCM 6

6

18

2

3

3

6

6

2 x 3

3

2

3

18

2 x 3 x 3

LCM 18

2 x 3 x 3 18

Lets Do More Examples!

Find the least common multiple of 9 and 12.

Method 1 Listing Multiples

No matter what method you choose, you get

the same answer.

9

9, 18, 27, 36, 45, 54, 63, 72, 81

12

12, 24, 36, 48

LCM 36

Method 2 Prime Factorization (Factor Trees)

9

12

9

3 x 3

3

3

3

4

12

2 x 2 x 3

3

2

2

2 x 2 x 3 x 3 36

LCM 36

More Examples Continued.

Find the LCM of 42 and 60.

Method 1 Listing

42

42, 84, 126, 168, 210, 252, 294, 336, 378, 420

60

60, 120, 180, 240, 300, 360, 420, 480

LCM 420

The next slide shows the same numbers using

factor trees.

More Examples Continued

Find the LCM of 42 and 60.

Method 2 Prime Factorization (Factor Trees)

42

60

6

7

6

10

2

3

2

5

2

3

7

42

2 x 3 x 7

60

2 x 2 x 5

LCM 420

X 3

2 x 2 x 3 x 5 x 7 420

Now You Try!

Find the LCM for 15 and 18 using either method.

Listing

15

15, 30, 45, 60, 75, 90, 105

LCM 90

18

18, 36, 54, 72, 90, 108, 126

Factor Trees

15

18

3

5

3

6

15

3 x 5

3

2

3

18

2 x 3 x 3

2 x 3 x 3 x 5 90

LCM 90

Now You Try Continued

Find the LCM 16 and 20 using either method.

Listing

16

16, 32, 48, 64, 80, 96, 112, 128, 144

LCM 80

20

20, 40, 60, 80, 100, 120, 140, 160

Factor Trees

16

20

16

2 x 2 x 2 x 2

5

4

4

4

20

2 x 2 x 5

5

2

2

2 x 2 x 2 x 2 x 5

2

2

2

2

LCM 80

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