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

Lesson 6.7Multiples and the Least Common Multiple

Start hereWords, worked example, and sentence starters

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.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
FactorSpanish: Factor A whole number that divides another number evenly, with no remainder. 6 divides 18 evenly.
MultipleSpanish: Múltiplo The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it. 6, 12, 18, 24
Greatest common factor (GCF)Spanish: Máximo común divisor (MCD) The largest number that is a factor of two or more numbers. It answers “how many equal groups can I make?” 48 and 36 share 1, 2, 3, 4, 6, 12 → GCF = 12
Least common multiple (LCM)Spanish: Mínimo común múltiplo (mcm) The smallest number that is a multiple of two or more numbers. It answers “when will these line up again?” 6, 12, 18, 24 and 8, 16, 24 → LCM = 24
Factor pairSpanish: Par de factores Two factors that multiply to make a number. In a word problem, one is the number of groups and the other is the size of each group. 48 = 2 × 24, so 2 packs of 24 pencils
Prime factorizationSpanish: Descomposición en factores primos Writing a number as a product of prime numbers, usually with a factor tree. Multiplying the primes two numbers share also gives the GCF. 48 = 2×2×2×2×3, 36 = 2×2×3×3 → shared 2×2×3 = 12

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A library van visits every 8 days and an art cart every 10 days. Both visit today. When do both visit again?

  1. Multiples of 8: 8, 16, 24, 32, 40.
  2. Multiples of 10: 10, 20, 30, 40.
  3. The first number on both lists is 40.

Answer: LCM = 40, so in 40 days

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The multiples of are .
  • The first multiple that both numbers share is .
  • The least common multiple is .
  • I used the LCM because the problem asks when .

Word bank multiplecommon multipleleast common multipleLCMskip-countlistsharefirstleastfactorrepeatat the same time

Watch out!A common mistake

A common mistake is reaching for the wrong tool: listing FACTORS for a problem about repeating cycles. Ayasha's classes repeat every 6 and 8 weeks, so the weeks they land on are multiples

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

Lesson 6.7Multiples and the Least Common Multiple

Apply Day · Version ASupported 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.

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

    Find the GCF of 15 and 25.

    Show your work

    Hint List the factors of 15 and of 25.

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

    Find the LCM of 3 and 4.

    Show your work

    Hint Skip-count by 3 and by 4. Find the first number in both lists.

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

    Find the GCF of 14 and 21.

    Show your work

    Hint List the factors of 14 and of 21. Find the greatest number in both lists.

    Final answer:
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 6.7Multiples and the Least Common Multiple

Apply Day · Version BCore 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.

  1. 1Circle the letter of the best answer. Show how you know.

    Buses leave every 15 minutes. Trains leave every 20 minutes. Both leave now. Which tells you when both leave together again?

    1. AThe LCM, 60 minutes
    2. BThe GCF, 5 minutes
    3. CThe sum, 35 minutes
    Show your work
  2. 2Complete each step, then write the final answer.

    Find the LCM of 9 and 12.

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

    Find the GCF of 20 and 45.

    Show your work
    Final answer:
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 6.7Multiples and the Least Common Multiple

Apply Day · ChallengeExtension

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.

  1. 1Circle the letter of the best answer. Show how you know.

    What is the greatest common factor of 18 and 24?

    1. A2
    2. B3
    3. C6
    4. D72
    Show your work
  2. 2Complete each step, then write the final answer.

    Raj says the LCM of 6 and 10 is 60 because 6 × 10 = 60. What is the LCM of 6 and 10?

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

    Find the LCM of 8 and 14.

    Show your work
    Final answer:
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