Lesson 18

Using Common Multiples and Common Factors

Let’s use common factors and common multiple to solve problems.

Problem 1

Mai, Clare, and Noah are making signs to advertise the school dance. It takes Mai 6 minutes to complete a sign, it takes Clare 8 minutes to complete a sign, and it takes Noah 5 minutes to complete a sign. They keep working at the same rate for a half hour.

  1. Will Mai and Clare complete a sign at the same time? Explain your reasoning.

  2. Will Mai and Noah complete a sign at the same time? Explain your reasoning.

  3. Will Clare and Noah complete a sign at the same time? Explain your reasoning

  4. Will all three students complete a sign at the same time? Explain your reasoning

Problem 2

Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.

  1. How many bags can he make without having any cookies left over?
  2. Find the another solution to this problem.
(From Unit 7, Lesson 16.)

Problem 3

  1. Find the product of 12 and 8.
  2. Find the greatest common factor of 12 and 8.
  3. Find the least common multiple of 12 and 8.
  4. Find the product of the greatest common factor and the least common multiple of 12 and 8.
  5. What do you notice about the answers to question 1 and question 4?
  6. Choose 2 other numbers and repeat the previous steps. Do you get the same results?

Problem 4

  1. Given the point \((5.5, \text-7)\), name a second point so that the two points form a vertical segment. What is the length of the segment?
  2. Given the point \((3, 3.5)\), name a second point so that the two points form a horizontal segment. What is the length of the segment?
(From Unit 7, Lesson 11.)

Problem 5

Find the value of each expression mentally.

  1. \(\frac12\boldcdot 37-\frac12 \boldcdot 7\)
  2. \(3.5\boldcdot 40+3.5\boldcdot 60\)
  3. \(999\boldcdot 5\)
(From Unit 6, Lesson 9.)