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

Lesson 6.76.7 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem — one step at a time, with support.

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. 1, 2, 4, 8, 16 divide 16.
MultipleSpanish: Múltiplo The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it. Multiples of 8: 8, 16, 24, 32, 40 …
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. 2 × 12 = 24
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. 24 = 2 × 2 × 2 × 3

How it worksWorked examplefinding the greatest common factor

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

Find the greatest common factor of 16 and 24.

  1. List the factors of 16. 1, 2, 4, 8, 16
  2. List the factors of 24. 1, 2, 3, 4, 6, 8, 12, 24
  3. Mark the factors that are in both lists. 1, 2, 4, 8
  4. Pick the greatest shared factor. GCF = 8

Answer: The greatest common factor of 16 and 24 is 8.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Find the greatest common factor of 20 and 35.

  1. List the factors of 20.
  2. List the factors of 35.
  3. Mark the factors that are in both lists.
  4. Pick the greatest shared factor. GCF =
Answer:greatest common factor of 20 and 35

Say it and write itSentence starters

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

  • The factors of are .
  • The factors that both numbers share are .
  • The greatest common factor is .
  • I used the GCF here because the problem asks for .

Word bank factorfactor paircommon factorgreatest common factorGCFprimeprime factorizationdivides evenlylistsharegreatestequal groups

Watch outA 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 — answering with the GCF of 2 claims a class that meets every 8 weeks happens in week 2. Use the size of the answer as a check: a GCF is never larger than the smaller number, and an LCM is never smaller than the larger one.

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

Lesson 6.76.7 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    NumberFactors
    181, 2, 3, 6, 9, 18
    241, 2, 3, 4, 6, 8, 12, 24
    Find the greatest factor in both lists.

    A coach has 18 apples and 24 granola bars. She makes snack bags that are all the same, with nothing left over. What is the greatest number of bags?

    1. 1List the factors of 18.
    2. 2List the factors of 24.
    3. 3Which factors are in both lists?
    4. 4What is the greatest common factor?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ActivityDays it happens
    Run, every 4 days4, 8, 12, 16, 20
    Swim, every 10 days10, 20, 30
    Find the first number in both lists.

    Juan runs every 4 days. He swims every 10 days. He does both today. In how many days will he do both on the same day again?

    1. 1List the multiples of 4.
    2. 2List the multiples of 10.
    3. 3What is the least number in both lists?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the GCF of 12 and 30.

    Show your work

    Hint List the factors of each number. Find the greatest number in both lists.

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

    Find the LCM of 6 and 9.

    Show your work

    Hint Skip-count by 6 and by 9. Find the first number in both lists.

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

    A store has 42 markers and 28 notebooks. It makes packs that are all the same, with nothing left over. What is the greatest number of packs?

    Show your work

    Hint The number of packs must divide both 42 and 28. Find the GCF.

    Final answer:
  6. 6Circle 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

    Hint Repeating times land on multiples. Do you need a factor or a multiple?

    Show your work

Explain your thinkingHow do you decide if a problem needs the GCF or the LCM? Use the snack bags and Juan's days to explain.

Sentence starter I use the GCF when ___. · I use the LCM when ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help