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2-5. Greatest Common Factor. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 2-5. Greatest Common Factor. Course 2. Learn to find the greatest common factor of two or more whole numbers. 2-5. Greatest Common Factor. Course 2. Insert Lesson Title Here. Vocabulary.

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2-5

Greatest Common Factor

Course 2

Warm Up

Problem of the Day

Lesson Presentation

2-5

Greatest Common Factor

Course 2

Learn to find the greatest common factor of two or more whole numbers.

2-5

Greatest Common Factor

Course 2

Insert Lesson Title Here

Vocabulary

greatest common factor (GCF)

2-5

Greatest Common Factor

Course 2

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

One way to find the GCF of two or more numbers is to list all the factors of each number. The GCF is the greatest factor that appears in all the lists.

2-5

Greatest Common Factor

Course 2

Additional Example 1:Using a List to Find the GCF

Find the greatest common factor (GCF).

12, 36, 54

List all of the factors of each number.

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

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Circle the greatest

factor that is in all

the lists.

54: 1, 2, 3, 6, 9, 18, 27, 54

The GCF is 6.

2-5

Greatest Common Factor

Course 2

Insert Lesson Title Here

Try This: Example 1

Find the greatest common factor (GCF).

14, 28, 63

List all of the factors of

each number.

14: 1, 2, 7, 14

28: 1, 2, 4, 7, 14, 28

Circle the greatest

factor that is in all

the lists.

63: 1, 3, 7, 9, 21, 63

The GCF is 7.

2-5

Greatest Common Factor

Course 2

Additional Example 2A: Using Prime Factorization to Find the GCF

Find the greatest common factor (GCF).

A. 40, 56

Write the prime factorization of

each number and circle the

common factors.

40 = 2 · 2 · 2 · 5

56 = 2 · 2 · 2 · 7

2 · 2 · 2 = 8

Multiply the common prime factors.

The GFC is 8.

2-5

Greatest Common Factor

Course 2

Additional Example 2B: Using Prime Factorization to Find the GCF

Find the greatest common factor (GCF).

B. 252, 180, 96, 60

Write the prime factorization

of each number and circle

the common prime factors.

252 = 2 · 2 · 3 · 3 · 7

180 = 2 · 2 · 3 · 3 · 5

96 = 2 · 2 · 2 · 2 · 2 · 3

60 = 2 · 2 · 3 · 5

2 · 2 · 3 = 12

Multiply the common prime

factors.

The GCF is 12.

2-5

Greatest Common Factor

Course 2

Insert Lesson Title Here

Try This: Example 2A

Find the greatest common factor (GCF).

A. 72, 84

72 = 2 · 2 · 2 · 9

Write the prime factorization of each number and circle the common factors.

84 = 2 · 2 · 7 · 3

2 · 2 = 4

Multiply the common prime factors.

The GCF is 4.

2-5

Greatest Common Factor

Course 2

Insert Lesson Title Here

Try This: Example 2B

Find the greatest common factor (GCF).

B. 360, 250, 170, 40

360 = 2 · 2 · 2 · 9 · 5

Write the prime factorization

of each number and circle

the common prime factors.

250 = 2 · 5 · 5 · 5

170 = 2 · 5 · 17

40 = 2 · 2 · 2 · 5

Multiply the common prime

factors.

2 · 5 = 10

The GCF is 10.

2-5

Greatest Common Factor

Course 2

Insert Lesson Title Here

Lesson Quiz: Part 1

Find the greatest common factor (GCF).

1. 28, 40

2. 24, 56

3. 54, 99

4. 20, 35, 70

4

8

9

5

2-5

Greatest Common Factor

Course 2

Insert Lesson Title Here

Lesson Quiz: Part 2

5. The math clubs from 3 schools agreed to a competition. Members from each club must be divided into teams, and teams from all clubs must be equally sized. What is the greatest number of members that can be on a team if Georgia has 16 members, William has 24 members, and Fulton has 72 members?

8

2-6

Least Common Multiple

Course 2

Warm Up

Problem of the Day

Lesson Presentation

2-6

Least Common Multiple

Course 2

Learn to find the least common multiple of two or more whole numbers.

2-6

Least Common Multiple

Course 2

Insert Lesson Title Here

Vocabulary

multiple

least common multiple (LCM)

2-6

Least Common Multiple

Course 2

The maintenance schedule on Ken’s pickup truck shows that the tires should be rotated every 7,500 miles and that the oil filter should be replaced every 5,000 miles. What is the lowest mileage at which both services are due at the same time? To find the answer you can use least common multiples.

2-6

Least Common Multiple

Course 2

A multiple of a number is a product of that number and a whole number. Some multiples of 7,500 and 5,000 are as follows:

7,500: 7,500, 15,000, 22,500, 30,000, 37,500, 45,000, . . .

5,000: 5,000, 10,000, 15,000, 20,000, 25,000, 30,000, . . .

A common multiple of two or more numbers

is a number that is a multiple of each of the

given numbers. So 15,000 and 30,000 are

common multiples of 7,500 and 5,000.

2-6

Least Common Multiple

Course 2

The least common multiple (LCM) of two or more numbers is the common multiple with the least value. The LCM of 7,500 and 5,000 is 15,000. This is the lowest mileage at which both services are due at the same time.

2-6

Least Common Multiple

Course 2

Additional Example 1: Using a List to Find the LCM

Find the least common multiple (LCM).

A. 2, 7

2: 2, 4, 6, 8, 10, 12, 14

List some multiples of each

number.

7: 7, 14, 21, 28, 35

Find the least value that is

in both lists.

The LCM is 14.

B. 3, 6, 9

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

List some multiples of each

number.

6: 6, 12, 18, 24, 30

9: 9, 18, 27, 36, 45

Find the least value that is

in all the lists.

The LCM is 18.

2-6

Least Common Multiple

Course 2

Insert Lesson Title Here

Try This: Example 1

Find the least common multiple (LCM).

A. 3, 7

List some multiples of each

number.

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

7: 7, 14, 21, 28

Find the least value that is

in both lists.

The LCM is 21.

B. 2, 6, 4

2: 2, 4, 6, 8, 10, 12, 14

List some multiples of each

number.

6: 6, 12, 18

4: 4, 8, 12

Find the least value that is

in all the lists.

The LCM is 12.

2-6

Least Common Multiple

Course 2

Additional Example 2A: Using Prime Factorization to Find the LCM

Find the least common multiple (LCM).

A. 60, 130

60 = 2 · 2 · 3 · 5

Write the prime factorization of

each number.

130 = 2 · 5 · 13

Circle the common prime factors.

List the prime factors, using

the circled factors only once.

2, 2, 3, 5, 13

2 · 2 · 3 · 5 · 13

Multiply the factors in the list.

The LCM is 780.

2-6

Least Common Multiple

Course 2

Additional Example 2B: Using Prime Factorization to Find the LCM

Find the least common multiple (LCM).

B. 14, 35, 49

Write the prime factorization of

each number.

14 = 2 · 7

35 = 5 · 7

Circle the common prime factors.

49 = 7 · 7

List the prime factors, using

the circled factors only once.

2, 5, 7, 7

Multiply the factors in the list.

2 · 5 · 7 · 7

The LCM is 490.

2-6

Least Common Multiple

Course 2

Insert Lesson Title Here

Try This: Example 2A

Find the least common multiple (LCM).

A. 50, 130

Write the prime factorization of

each number.

50 = 2 · 5 · 5

Circle the common prime factors.

110 = 2 · 5 · 11

List the prime factors, using

the circled factors only once.

2, 5, 5, 11

2 · 5 · 5 · 11

Multiply the factors in the list.

The LCM is 550.

2-6

Least Common Multiple

Course 2

Insert Lesson Title Here

Try This: Example 2B

B. 18, 36, 54

Write the prime factorization of

each number.

18 = 2 · 3 · 3

Circle the common prime factors.

36 = 2 · 2 · 3 · 3

54 = 2 · 3 · 3 · 3

List the prime factors, using

the circled factors only once.

2, 2, 3, 3, 3

2 · 2 · 3 · 3 · 3

Multiply the factors in the list.

The LCM is 108.

2-6

Least Common Multiple

Course 2

Mr. Washington will set up the band chairs all in rows of 6 or all in rows of 8. What is the least number of chairs he will set up?

Find the LCM of 6 and 8.

6 = 2 · 3

8 = 2 · 2 · 2

The LCM is 2 · 2 · 2 · 3 = 24.

He will set up at least 24 chairs.

2-6

Least Common Multiple

Course 2

Insert Lesson Title Here

Try This: Example 3

Two satellites are put into orbit over the same location at the same time. One orbits the earth every 24 hours, while the second completes an orbit every 18 hours. How much time will elapse before they are once again over the same location at the same time?

Find the LCM of 24 and 18.

24 = 2 · 2 · 2 · 3

18 = 2 · 3 · 3

The LCM is 2 · 2 · 2 · 3 · 3 = 72.

2-6

Least Common Multiple

Course 2

Insert Lesson Title Here

Lesson Quiz

Find the least common multiple (LCM).

1. 18, 21

3. 4, 6, 15

5. You are planning a picnic. You can purchase paper plates in packages of 30, paper napkins in packages of 50, and paper cups in packages of 20. What is the least number of each type of package that you can buy and have an equal number of each?

126

2. 24, 27

216

16

4. 4, 8, 16

60

10 packages of plates

6 packages of napkins

15 packages of cups