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

Lesson 6.7Find Factors and Multiples

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

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.

Why This Matters The station quartermaster has two jobs today. First, split the pencil and notebook stock into identical combo packs with nothing left over — that is a factor question. Second, work out when two supply runs that repeat on different cycles will land in the same week — that is a multiple question. Same lesson, opposite tools. Today the stock is 24 pencils and 36 notebooks. One supply run arrives every 6 days and another arrives every 8 days.

RememberFind Factors and Multiples

Greatest Common Factor (GCF) & Least Common Multiple (LCM) A factor divides a number evenly, so factors answer questions about splitting a stock into equal groups. A multiple is where you land when you skip-count, so multiples answer questions about when repeating events line up.

  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)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which expression is equivalent to 5x + 2x?

    1. A7x
    2. B7x²
    3. C10x
    4. D52x
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which expression is NOT equivalent to 2y + 2y + 2y?

    1. A2y³
    2. B2y × 3
    3. C3(2y)
    4. D6y
    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Are 3(n + 2) and 3n + 6 equivalent? Test with n = 4.

    1. ANo — one is 18 and one is 14
    2. BYes — both equal 18
    3. CYes, but only when n = 0
    4. DYou cannot test with a number
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Simplify 6a + 4 − 2a.

    1. A2a + 4
    2. B4a + 4
    3. C4a
    4. D8a
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The school store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of pencils and the same number of notebooks, using all the stock with nothing left over. What is the GCF of 48 and 36?

    1. A4
    2. B6
    3. C12
    4. D144
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    The school store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of pencils and the same number of notebooks, using all the stock with nothing left over. What is the LCM of 6 and 8?

    1. A2
    2. B14
    3. C24
    4. D48
    Show your work

Explain your thinkingBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?

Sentence starter If the problem ___ something into equal groups, I use the ___. If it asks when things ___ again, I use the ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.7Find Factors and Multiples

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

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.

Why This Matters The station quartermaster has two jobs today. First, split the pencil and notebook stock into identical combo packs with nothing left over — that is a factor question. Second, work out when two supply runs that repeat on different cycles will land in the same week — that is a multiple question. Same lesson, opposite tools. Today the stock is 24 pencils and 36 notebooks. One supply run arrives every 6 days and another arrives every 8 days.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each pair to its greatest common factor.

    1. 12 and 18
    2. 48 and 36
    3. 10 and 15
    4. 7 and 9
    • A6
    • B12
    • C5
    • D1
  2. 2Write the name of the correct group on each line.

    Sort each statement about factors and multiples.

    Groups: True of factors True of multiples
    • Never larger than the number
    • Never smaller than the number
    • There is a limited number of them
    • The list goes on forever
    • Found by dividing
    • Found by skip-counting
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    The school store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of pencils and the same number of notebooks, using all the stock with nothing left over. A problem asks when two repeating schedules meet again. Which do you use?

    1. AThe least common multiple
    2. BThe greatest common factor
    3. CEither one works
    4. DNeither — you list factors
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Is 4 a factor or a multiple of 12?

    1. AA factor
    2. BA multiple
    3. CBoth
    4. DNeither
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    What is the GCF of 10 and 15?

    1. A1
    2. B5
    3. C10
    4. D30
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1ProblemList the factors of 16.
    2. 2Step 116 = 1 × 16, 2 × 8, 4 × 4
    3. 3Step 2So the factors are 2, 4, and 8.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help