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Number System:

Number System:. Thinking Logically About Multiplicative Arithmetic 6NS4 Lesson 3: Least Common Multiple and Greatest Common Factor Engage NY Module 2 Lesson D 18 kp. Opening Exercise.

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Number System:

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  1. Number System: Thinking Logically About Multiplicative Arithmetic 6NS4 Lesson 3: Least Common Multiple and Greatest Common Factor Engage NY Module 2 Lesson D 18 kp kp

  2. Opening Exercise The Greatest Common Factor of two whole numbers is the greatest whole number which is factor of both numbers. The Least Common Multiple of two numbers is the least whole number which is a multiple of both numbers.

  3. Find the Greatest Common Factor of 12 and 18. Start with one times the number Circle all the common factors Put a triangle around the Greatest Common Factor 12 18

  4. Find the Least Common Multiple of 12 and 18. List the first ten multiples of each number.

  5. Exploratory Challenge 1Factors and GCF Find the Greatest Common Factor of 30 and 50 3050

  6. Find the GCF of 30 and 45 30 45

  7. There are 18 girls and 24 boys who want to participate in a Trivia Challenge. If each team must have the same ratio of girls and boys, what is the greatest number of teams that can enter? How many boys and girls will be on each team? 18 Girls 24 Boys Six teams of three girls and four boys each.

  8. The Ski Club members are preparing identical welcome kits for the new skiers. The Ski Club has 60 hand warmer packets and 48 foot warmer packets. What is the greatest number of identical kits they can prepare using all of the hand warmer and foot warmer packets? 60 Hand Warmers 48 Foot Warmers 1 Twelve packets with five Hand Warmers and four Foot Warmers each.

  9. 16 4 Is the GCF of a pair of numbers ever equal to one of the numbers? Explain with an example. Yes, when the smaller of the two numbers is a factor of the greater number and the greater of the two numbers is a multiple of the lesser number.

  10. Is the GCF of a pair of numbers ever greater than both numbers? Explain with an example. No. Factors are always less than or equal to the number so the GCF can never be greater than both numbers. See above example.

  11. Exploratory Challenge 2Multiples and LCM Find the Least Common Multiple of 9 and 12 Find the LCM of 8 and 18

  12. Starting at 6:00 a.m., a bus makes a stop at my street corner every 15 minutes. Also starting at 6:00 a.m., Bus Taxi a taxi cab comes by every 12 minutes. What is the next time there will be a bus and a taxi at the corner at the same time? 7:00 a.m., which is 60 minutes after 6:00. LCM of 12, 15 = 60

  13. Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has 24 teeth and the second gear has 40 teeth, how many revolutions of the first gear are needed until the marks line up again? Five revolutions of the first gear.

  14. Is the LCM of a pair of numbers ever equal to one of the numbers? Explain with an example. Yes. If the smaller number is a factor of the larger number.

  15. Is the LCM of a pair of numbers ever less than both numbers? Explain with an example. No. Multiples are always equal to or greater than the number.

  16. Exploratory Challenge 3 Using a factor tree and prime factors, find the GCF of 30 and 50. 30 50 215 5 10 3 525 Common factors are 2 and 5, GCF is 2 x 5 = 10

  17. Exploratory Challenge 3 . Find the LCM of 30 and 50. Compare the product of the GCF and LCM to the product of the numbers. 10 x 150 = 1500 30 x 50 = 1500 GCF x LCM will always equal the product of the numbers

  18. Exploratory Challenge 4 Find the GCF of the two addends and rewrite using the Distributive Property. 12 + 18 = GCF = 6 12 + 18 = 6(2) + 6(3) = 6(2 + 3) = 30

  19. Exploratory Challenge 4 Find the GCF of the two addends and rewrite using the Distributive Property. 42 + 14 = GCF = 7 42 + 14 = 7(6) + 7(2) = 7(6 + 2) = 56

  20. Exploratory Challenge 4 Find the GCF of the two addends and rewrite using the Distributive Property. 36 + 27 = GCF = 9 36 + 27 = 9(4) + 9(3) = 9(4 + 3) = 63

  21. Problem Set 1. Find the LCM and GCF of 12 and 15. 2. Write two numbers, neither of which is 8, whose GCF is 8. 3. Write two numbers, neither of which is 28, whose LCM is 28. 4. Find the GCF of 96 and 144 5. There are 435 representatives and 100 senators serving in the United States Congress. How many identical groups with the same numbers of representatives and senators could be formed from all of Congress, if we want the largest groups possible?

  22. 6. Find the LCM of 12 and 30 7. Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic, with none left over, what is the least amount of each we need to buy? 8. Find the GCF of the two addends and rewrite using the Distributive Property. a. 16 + 72 = b. 44 + 33 =

  23. Extra Problem Slides There are 435 representatives and 100 senators serving in the United States Congress. How many identical groups with the same numbers of representatives and senators could be formed from all of Congress, if we want the largest groups possible? Representatives Senators Five groups with 87 Representatives and 20 Senators in each.

  24. Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic, with none left over, what is the least amount of each we need to buy? Hot Dogs Buns Four packages of hot dogs and five packages of buns.

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