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.

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?

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.

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.

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.

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?

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.

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.

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.

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

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.