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

Lesson 6.76.7 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    236251060
    The tree breaks 60 into primes: two 2s, one 3, one 5.

    Use prime factors to find the GCF of 60 and 84.

    1. 1Use the factor tree. Write 60 as a product of primes.
    2. 2Write 84 as a product of primes.
    3. 3Multiply the primes both numbers share. What is the GCF?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ItemTotals you can buy
    Rolls, packs of 1212, 24, 36
    Patties, packs of 88, 16, 24, 32
    Find the first total in both lists.

    Rolls come in packs of 12. Patties come in packs of 8. You want the same number of rolls and patties. How many packs of each should you buy?

    1. 1Do you need the GCF or the LCM?
    2. 2What is the LCM of 12 and 8?
    3. 3How many packs of each?
    4. 4Why not use 12 × 8 = 96?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the LCM of 9 and 12.

    Show your work
    Final answer:
  4. 4Complete 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:
  5. 5Complete each step, then write the final answer.

    Ms. Diaz has 56 red tiles and 70 blue tiles. She makes identical sets with no tiles left over. What is the greatest number of sets?

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingOne problem says 'equal groups with nothing left over.' Another says 'the same number from packs.' Which needs the GCF and which needs the LCM? Why?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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