Wednesday, October 13 (Blue)Thursday, October 14 (Gold)

1. Fill in planner (Practice 5-1)2. Bell Work (Write the prime factorization of

each number)

Objective

• SWBAT find the Least Common Multiple (LCM) and compare and order fractions.

Vocabulary

Multiple

least common multiple (LCM)

least common denominator (LCD)

A multiple of a number is the product of the number and any nonzero whole number.

multiple

least common multiple (LCM): The smallest number that is a multiple of two or more numbers.

least common denominator (LCD): The smallest number that is the multiple of two or more denominators.

Today, the school’s baseball and soccer teams had games. The baseball team plays every 7 days. The

soccer team plays every 3 days. When will the teams have games on the same day again?

7: 7, 14, 21 , 28, 35, 42, . . .

3: 3, 6, 9, 12, 15, 18, 21, . . .

LCM: 21. In 21 days, both teams will have game on the same day again.

List multiples of 3 and 7.

Find the smallest number that is in all the lists.

3,7

The prime factorization of a number is the number written as a product of its prime factors.

Remember!

Example 2: Find the LCM of 16 and 36

16 = 24

36 = 22• 32

Write the prime factorizations

Use the greatest power of each factor.

24 • 32

16 • 9 = 144Multiply.

LCM: 144

Example 3: Find the LCM of 5a4 and 15a

5a4 = 5 • a4

15a = 3• 5 •aWrite the prime factorizations

Use the greatest power of each factor.

3 • 5• a4

15a4 Multiply.

LCM: 15a4

negative positive

7 77

7-7

7

84

84

21

21

21

84

28

28

56

84

< < < < <

12 20 60

48 45 180

60 456m 275xy

> < <

3

2,

12

5,6

1

12

7,2

1,

10

3,5

1

Additional Example 2D: Using Multiples to Find the LCM

Find the least common multiple (LCM).

15, 6, and 4

15 = 3 • 5

4 = 22

Write the prime factorization of each number in exponential form.

3 • 5 • 22

3 • 5 • 22 = 60

To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations.

6 = 3 • 2

LCM: 60

Check It Out: Example 2A

Find the least common multiple (LCM).

Method 1: Use a number line.

2 and 3Use a number line to skip count by 2 and 3.

0 1 2 3 4 5 6

The least common multiple (LCM) of 2 and 3 is 6.

Check It Out: Example 2B

Find the least common multiple (LCM).

Method 2: Use a list.

3, 4, and 9

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

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, …

9: 9, 18, 27, 36, 45, . . .

The least common multiple of 3, 4, and 9 is 36.

List multiples of 3, 4, and 9.

Find the smallest number that is in all the lists.

Check It Out: Example 2C

Find the least common multiple (LCM).

Method 3: Use prime factorization.

4 and 10

4 = 2 • 210 = 2 • 5

Write the prime factorization of each number.

Line up the common factors. 2 • 2 • 5

2 • 2 • 5 = 20To find the LCM, multiply one number from each column.

LCM: 20

Check It Out: Example 2D

Find the least common multiple (LCM).

12, 6, and 8

12 = 22 • 3

6 = 2 • 3Write the prime factorization of each number in exponential form.

23 • 3

23 • 3 = 24

To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations.

8 = 23

LCM: 24

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