Greatest Common Factor (GCF)Least Common Multiple (LCM)

Chapter 1, Lesson 1

ObjectivesThe student will be able to:

1. Find the prime factorization of a number.2. Find the GCF for two or more numbers.3. Find the LCM for two or more numbers.

Designed by Skip Tyler, Varina High School

What are prime factors of:

75

48

50

What are multiples of (list the first 5):

5

7

10

A prime number is a number that can be divided

only by one and itself.Factor A number that divides

other numbers evenly.What are the prime factors of

20?2, 2, 5

GCF Greatest Common Factor is used to find the

common factor between two or more numbers. The factor does NOT have to be prime.

Find the GCF between: 10 & 20

28 & 42

1) Find the GCF of 12 & 18.

2) Find the GCF of 12 & 66

Now you try it.1) Find the GCF of 18 & 30.

2) Find the GCF of 32 & 48.

Multiple The product of a whole number multiplied times any other whole number.

Ex: Find the first five multiples of 3.

Common Multiple A number that is a multiple of two or more numbers.

Some multiples of 3 & 6

3 3, 6, 9, 12, …

6 6, 12, 18, …

Least Common Multiple The smallest common multiple of a set of two or more numbers.

6 = 6, 12, 18, 24, 30, 36 5 = 5, 10, 15, 20, 25, 30

1) Find the LCM of 2 & 3.

2) Find the LCM for 14 & 21.

1) Find the LCM for 2, 6.

2) Find the LCM of 4, 5, 10.

Now you try it.

GCF Story ProblemsKeywords: greatest, most

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?

Since they are asking about the “Greatest” number of servings, we are going to find the GCF.10 = 2 * 515 = 3 * 520 = 2 * 2 * 5

CakesType Number of ServingsMarble 10Red velvet 15Chocolate 20

GCF = 5Each row will get 5 servings

How many rows of 5 pieces in each cake? Think about it this way:

If each row has 5 pieces, how many rows are there in the marble cake of 10 servings?

If each row has 5 pieces, how many rows are there in the red velvet cake of 15 servings?

If each row has 5 pieces, how many rows are there in the chocolate cake of 20 servings?

2

3

4

LCM Story ProblemsKeywords: future expressions

Do you remember this?All you have to do is find the LCM for this kind of problem.

9: 9, 18, 27, 32, … 3: 3, 6, 9, 12, …

Solve Lana earned $49 on Friday, $42 on

Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? How many bracelets she sold on each day?

Solve 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?