Warm UpWrite the first five multiples of each number.

1) 5

2) 6

3)10

4)12

5, 10, 15, 20, 25

6, 12, 18, 24, 30

10, 20, 30, 40, 50

12, 24, 36, 48, 60

9.23.13

Learning Goal: I will be able to find the (LCM) least common multiple of a group of numbers.

Topic: Least Common Multiples (LCM)

Least Common Multiple (LCM)

• The least common multiple is the smallest number that is common between two lists of multiples.

Find the least common multiple (LCM) of 3 and 4

Method 1: use a number line

Use a number line to skip count by 3 and 4.

0 2 4 6 8 10 12

The least common multiple (LCM) of 3 and 4 is 12.

Method 2: Use a list.Example 1:

Find the LCM of 12 and 18The 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

10, 20, 30, 40, 50, 60, 70, 80If you don’t see a common multiple, make each list go further.

81, 90, 99

90, 100, 110

The LCM of 9 and 10 is 90

Example 3:Find the LCM of 4 and 12

4, 8, 12, 16

12, 24, 36Answer: 12

Example 4:Find the LCM of 5 and 8

5, 10, 15, 20, 25, 30

8, 16, 24, 32, 40, 48

35, 40

Answer: 40

Method 3: Use prime factorization.

Find the least common multiple (LCM).

6 and 20

6 = 2 • 320 = 2 • 2 • 5

Write the prime factorization of each number.

Line up the common factors. 2 • 3 • 2 • 5

2 • 3 • 2 • 5 = 60

To find the LCM, multiply one number from each column.

LCM: 60

Classwork:Worksheet page 29

Quiz: Prime, Composite, Prime Factorization, Common Factors, GCF and LCM on Wednesday, 9/25/13

Lesson Quiz

Find the least common multiple (LCM).

1. 6, 14 2. 9, 12

3. 5, 6, 10 4. 12, 16, 24, 36

5. Two students in Mrs. Albring’s preschool class are

stacking blocks, one on top of the other. Reece’s

blocks are 4 cm high and Maddy’s blocks are 9 cm

high. How tall will their stacks be when they are the

same height for the first time?

36 cm

42 36

30 144