Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.7Multiples and the Least Common Multiple

Apply Day · Set BSecond form · new problems, same idea

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Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.

Remember6.7 · Part II

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

  1. GCF: Largest factor shared by two numbers — used to simplify fractions or divide into equal groups
  2. LCM: Smallest shared multiple — used to find common denominators
  3. Use prime factor trees or list method to find common factors/multiples

Words: Factor (Factor)Multiple (Múltiplo)Greatest common factor (GCF) (Máximo común divisor (MCD))Least common multiple (LCM) (Mínimo común múltiplo (mcm))Factor pair (Par de factores)

  1. 1Complete each step, then write the final answer.

    Find the GCF of 12 and 30.

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find the LCM of 6 and 9.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    The GCF of 18 and a number n is 9. The number n is between 20 and 30. What is n?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Napkins come in packs of 6. Plates come in packs of 15. You want the same number of napkins and plates. What is the least number of each you can buy?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A florist has 45 roses and 60 daisies. She makes identical bunches with no flowers left over. What is the greatest number of bunches?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Two numbers have a GCF of 4 and an LCM of 24. One number is 8. What is the other number?

    Show your work
    Final answer:
  7. 7Circle the letter of the best answer. Show how you know.

    Which list shows all the factors of 12?

    1. A1, 2, 3, 4, 6, 12
    2. B1, 12
    3. C2, 3, 4, 6
    4. D12, 24, 36, 48
    Show your work
  8. 8Circle the letter of the best answer. Show how you know.

    Which list shows the first four multiples of 8?

    1. A1, 2, 4, 8
    2. B2, 4, 6, 8
    3. C8, 16, 24, 32
    4. D8, 9, 10, 11
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

    What is the greatest common factor of 12 and 18?

    1. A2
    2. B3
    3. C6
    4. D36
    Show your work
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