1. 10/13/08 GCF, LCM Word Problems #20
Warm-up
Nicholas bikes every third day and skates every other day. Today is April 5, and Nicholas biked and skated. On what date will he both bike and skate?
April 11
Today’s Plan:
Warm-up and tests back
GCF & LCM word problems
Assignment:Problem Solving 2-5 & 2-6
Both sides, odds or evens all on graph paper showing all work including factor tree and prime factorization line up.

2. Additional Example 3: Problem Solving Application
Course 2
2-5
Greatest Common Factor
Additional Example 3: Problem Solving Application
You have 120 red beads, 100 white beads, and 45 blue beads. You want to use all the beads to make bracelets that have red, white, and blue beads on each. What is the greatest number of matching bracelets you can make?

3. Understand the Problem
Course 2
2-5
Greatest Common Factor
Additional Example 3 Continued 1
Understand the Problem
Rewrite the question as a statement.
• Find the greatest number of matching bracelets you can make.
List the important information:
• There are 120 red beads, 100 white beads,
and 45 blue beads.
• Each bracelet must have the same
number of red, white, and blue beads.
The answer will be the GCF of 120, 100, and 45.

4. Additional Example 3 Continued
Course 2
2-5
Greatest Common Factor
Additional Example 3 Continued 2
Make a Plan
You can list the prime factors of 120, 100,
and 45 to find the GFC.
Solve 3
120 = 2 · 2 · 2 · 3 · 5
100 = 2 · 2 · 5 · 5
45 = 3 · 3 · 5
The GFC of 120, 100, and 45 is 5.
You can make 5 bracelets.

5. Additional Example 3 Continued
Course 2
2-5
Greatest Common Factor
Additional Example 3 Continued
Look Back 4
If you make 5 bracelets, each one will have
24 red beads, 20 white beads, and 9 blue
beads, with nothing left over.

6. Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Try This: Example 3
Nathan has made fishing flies that he plans to give away as gift sets. He has 24 wet flies and 18 dry flies. Using all of the flies, how many sets can he make?

7. Understand the Problem
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Try This: Example 3 Continued 1
Understand the Problem
Rewrite the question as a statement.
• Find the greatest number of sets of flies
he can make.
List the important information:
• There are 24 wet flies and 18 dry flies.
• He must use all of the flies.
The answer will be the GCF of 24 and 18.

8. Try This: Example 3 Continued
Course 2
2-5
Greatest Common Factor
Try This: Example 3 Continued 2
Make a Plan
You can list the prime factors of 24 and 18
to find the GCF.
Solve 3
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
Multiply the prime factors that are common to both 24 and 18.
2 · 3 = 6
You can make 6 sets of flies.

9. Greatest Common Factor Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Try This: Example 3 Continued
Look Back 4
If you make 6 sets, each set will have
3 dry flies and 4 wet flies.

10. Greatest Common Factor Insert Lesson Title Here
Course 2
2-5
Greatest Common Factor
Insert Lesson Title Here
Lesson Quiz: Part 2
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

11. Insert Lesson Title Here
Course 2
2-6
Least Common Multiple
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.