© Edgenuity, Inc. 1

Warm-Up Factors and Multiples

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

Lesson Goals

Learn about the greatest common factor (GCF)and the least common multiple (LCM).

Solve real-world

problems using the

and the

LCM.

Find the

of two numbers.

Find the GCF of

numbers.

WK2

Lesson Question

?

greatest common factor (GCF)

the whole number that evenly divides

into (is a factor of) two or more numbers

least common multiple (LCM)

the whole number that two or more whole

numbers will evenly into

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Warm-Up Factors and Multiples

Factors

A factor is a number that divides evenly into a number.

Find the multiplication facts that equal 16.

1 × 16 =     2 × = 16    4 × = 16

Factors of 16: 1, 2, 4, , 16

Words to KnowWK2

multiplethe of a number and any nonzero whole

number

relatively primetwo or more whole numbers whose greatest

factor is

© Edgenuity, Inc. 3

Instruction Factors and Multiples

The Greatest Common Factor

The greatest common factor (GCF) is the whole number that evenly divides into two or more numbers.

Find the GCF of 8 and 12.

1. the factors of

both numbers.

2. Circle the factors.

3. Identify the greatest common factor.

Prime Factorization and GCF

You can also use the prime factorization to find the GCF of two numbers.

Find the GCF of 18 and 30.

1. Write the

factorization of each number.

2. Circle the common prime factors.

3. Find the of

the common prime factors.

2 × = 6

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 30: 2 × 3 × 5

The GCF of 18 and 30 is .

2Slide

4

Circle the common factors.

Factors of 8: 1, 2, 4, 8

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

The GCF of 8 and 12 is .

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Instruction Factors and Multiples

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9

Relatively Prime Numbers

Find the GCF of 10 and 21.

Circle the common factors.

Factors of 10: 1, 2, , 10

Factors of 21: 1, 3, 7, 21

The only factor common to both of these numbers is the factor 1.

The GCF of 10 and 21 is .

Two numbers are relatively prime if the of the numbers is 1.

Multiples

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

Multiples of 4: 4, , 12, , 20…

10 is not a multiple of 4 because there is no whole number that can be multiplied by 4 to get the product 10.

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Instruction Factors and Multiples

9Slide

The Least Common Multiple

The least common multiple (LCM) is the whole number that two or

more whole numbers will evenly divide into.

Find the LCM of 4 and 6.

1. List multiples of each number.

2. Circle common multiples.

3. Identify the least common multiple.

Circle the common multiples.

Multiples of 4: 4, 8, 12, 16, 20

Multiples of 6: 6, 12, 18, 24,

The LCM of 4 and 6 is .

Using GCF to Solve Word Problems

A florist has 24 red roses and 36 white roses. She plans to use all the flowers and make arrangements that look the same. Each vase will have the same number of each color of rose. How many vases will she need?

Find the GCF of 24 and 36 using the prime factorization method.

Circle the common prime factors.

Prime factorization of 24: 2 × 2 × 2 × 3

Prime factorization of 36: 2 × 2 × 3 × 3

Product of the common prime factors: 2 × × 3 = 12

is the GCF for the numbers 24 and 36.

The florist will need 12 in order to get identical flower arrangements in each vase.

12

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Instruction Factors and Multiples

14

12Slide

A florist has 24 red roses and 36 white roses. She plans to use all the flowers and make arrangements that look the same. Each vase will have the same number of each color of rose. How many roses of each color will be in each vase?

We previously found that the GCF of 24 and 36 is 12, and the florist is using 12 vases.

Use division to separate each group of roses into 12 vases.

red white

24 ÷ 12 = 36 ÷ = 3

There will be red and white roses in each vase.

Using LCM to Solve Problems

The flower shop has a special promotion this month. Every 3rd customer gets a free rose, and every 8th customer gets $5 off a flower arrangement. Which customer will be the 1st to receive a free rose and $5 off a purchase?

Use the .

1. List the first five multiples of each number.

Multiples of 3: 3, 6, , 12, 15

Multiples of 8: 8, 16, , 32, 40

2. Find the least common multiple.

Since we did not find a common multiple, we continue adding multiples of 3.

3, 6, 9, 12, 15, 18, , 24

is the LCM of the values 3 and 8.

The 24th customer will be the first customer to receive both offers.

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Summary Factors and Multiples

? Lesson Question

How can you use the greatest common factor and the least common multiple to solve problems?

Answer

Review: Key Concepts

• The greatest common factor (GCF) is the whole number that evenly divides into two or more numbers.

• Factors of 8: 1, 2, , 8

• Factors of 12: 1, 2, 3, 4, 6, 12

The GCF of 8 and 12 is .

• Two numbers are relatively if their GCF is 1.

• The least common multiple (LCM) is the whole number that two or more whole numbers can divide into.

• Multiples of 4: 4, , 12, 16, 20, . . .

• Multiples of 6: 6, 12, 18, 24, 30, . . .

The LCM of 4 and 6 is 12.

2

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Summary Factors and Multiples

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