Factors

Ratios and Proportional Relationships

Course 1, Lesson 1-1

•To find the greatest common
factor (GCF)
•To find the least common
multiple (LCM)

Ratios and Proportional Relationships

Course 1, Lesson 1-1

•greatest common factor
• least common multiple

Ratios and Proportional Relationships

Course 1, Lesson 1-1

Ratios and Proportional Relationships

Course 1, Lesson 1-1

Ratios and Proportional Relationships

Course 1, Lesson 1-1

Ratios and Proportional Relationships

Course 1, Lesson 1-1

Ratios and Proportional Relationships

Course 1, Lesson 1-1

Ratios and Proportional Relationships

Course 1, Lesson 1-1

There are one-slice servings of three types of
cake on a table. Each row has an equal
number of servings and only one type
of cake. What is the greatest number
of servings in each row?

1.

To solve this problem, use common factors.

2factors of 10: 1, 2, 5, 10

3factors of 15: 1, 3, 5, 15

4

5The GCF of 10, 15, and 20 is 5. So, the greatest number of
pieces of cake that can be placed in each row is 5.

Need Another Example?

factors of 20: 1, 2, 4, 5, 10, 20

1

The common factors are 1 and 5.

15

1 5

1 5

Step-by-Step Example

2. Find the GCF of 12 and 18.

2 and 3 are the common
prime factors.

1

So, the GCF of 12 and 18 is 2 × 3, or 6.

Need Another Example?

2

12

18

6 × 2

2

9 ×

2

2

3

2

3

3

×

×

×

×

Step-by-Step Example

Answer

Warren has 60 carrot sticks and 42 celery
sticks. He wants to package them in plastic
bags so that each bag has an equal number
of carrot sticks and an equal number of celery
sticks. What is the greatest number of bags
he can put together?

Need Another Example?

Need Another Example?

Need Another Example?

3. Find the LCM of 2 and 3.

1

Need Another Example?

2

3

4
1 × 2, 2 × 2, 3 × 2,…

5

Use a number line.

Put a red X above each multiple of 2 and a blue X above each
multiple of 3.

The least number with both a red and a blue X is 6.
So, 6 is the least common multiple of 2 and 3.

Use an organized list.

List the nonzero multiples of 2 and 3.

multiples of 2: 2, 4, 6, 8, 10, 12,…
multiples of 3: 3, 6, 9, 12, 15,…
1 × 3, 2 × 3, 3 × 3,…

Notice that 6 and 12 are common multiples.
So, the least common multiple of 2 and 3 is 6.

6 12

6 12

Step-by-Step Example

Find the least common multiple of 9 and 21.

Answer

Need Another Example?

4. Find the LCM of 14 and 21 using prime factorization.

1

Need Another Example?

2

7 is the only common prime factor.

3

4

Write the prime factorization of each number.

Multiply using each common prime factor only once.

So, the LCM is 7 × 2 × 3 or 42.

14

21

7

7

×

×

2

3

Step-by-Step Example

Find the least common multiple of 4, 6, and 8.

Answer

Need Another Example?

1

Need Another Example?

2

3

5.

multiples of 2: 2, 4, 6, 8, 10, 12, 14,…

multiples of 5: 5, 10, 15, 20, 25, 30,…

The least common multiple of 2 and 5 is 10. So, Ernesto and
Kamala will see each other again in 10 weeks.

Ernesto has painting class every 2 weeks. Kamala
has a pottery class every 5 weeks. Ernesto and
Kamala met at the art building for class this week. How
many weeks will it be until they see each other again?

Step-by-Step Example

Answer

Need Another Example?

At the grand opening of a store, every sixth
customer to enter the store is given a $10 gift
certificate and every ninth customer is given a
coupon for 10% off their total purchase. Which
customer will receive both gifts?

Find the least common

multiple of 10, 12, and 15.

Ratios and Proportional Relationships

Ratios and Proportional Relationships

Course 1, Lesson 1-1