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GCF & LCM: Factors and Multiples

Sixth graders find the greatest common factor (GCF) and least common multiple (LCM) of two numbers — powerful tools for simplifying fractions, finding common denominators, and solving real problems.

Grade 6Number Theory50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Find the GCF of two numbers.
  • ✓Find the LCM of two numbers.
  • ✓Tell factors from multiples.
  • ✓Use them to solve problems.
Essential Question

Two numbers can share factors and share multiples. What’s the biggest factor they have in common — and the smallest multiple? And why does it matter?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

GCF or LCM?

Project each item and have students find the GCF or LCM. The tool explains the difference between the two.

🔢 Find the GCF and LCMTry it
Find the GCF or LCM for each pair.
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Shared Factors

5 min

Two numbers share factors and multiples — what’s biggest and smallest?

👩‍🏫 Teacher Moves

  • Show factors and multiples.
  • Ask what they share.
  • Set the goal: GCF and LCM.

🎒 Student Actions

  • See the lists.
  • Find shared ones.
  • Predict the idea.
2

I Do — GCF vs. LCM

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • List factors; find the GCF.
  • List multiples; find the LCM.
  • Contrast the two.

🎒 Student Actions

  • Find the GCF.
  • Find the LCM.
  • Tell them apart.
3

We Do — Solve Together

13 min

Class uses GCF or LCM?

👩‍🏫 Teacher Moves

  • Find each GCF/LCM.
  • Explain the method.
  • Say which is which.

🎒 Student Actions

  • Find each.
  • Explain it.
  • Name it.
4

You Do — On Your Own

12 min

Students find GCF/LCM.

👩‍🏫 Teacher Moves

  • Find GCF and LCM.
  • Simplify a fraction with the GCF.
  • Solve a word problem.

🎒 Student Actions

  • Find them.
  • Simplify one.
  • Solve one.
5

Close — Close

5 min

One pair.

👩‍🏫 Teacher Moves

  • Give two numbers.
  • Find GCF and LCM.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find them.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
6.NS.4

Find the GCF of two numbers ≤ 100 and the LCM of two numbers ≤ 12.

CCSS
6.NS.4

Use the distributive property with the GCF.

CCSS
6.EE.2

Write and evaluate numerical expressions.

SMP
MP.7

Look for and make use of structure in factors and multiples.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • List factors and multiples visually.
  • Sentence frame: “The GCF/LCM is ___.”
  • Use factor rainbows.

Support & Access

IEP / 504
  • Start with small numbers.
  • List factors together.
  • Circle the shared ones.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Use prime factorization.
  • Apply GCF to simplify fractions.
  • Use LCM for common denominators.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Number charts
  • 💻GCF or LCM?
  • 📄Factor sheets
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

factora number that divides evenlymultiplea product of a numberGCFgreatest common factorLCMleast common multiplecommonshared by bothprime factorizationa number as a product of primesdivide evenlyno remainderdistributive propertya(b+c)=ab+ac
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is the GCF of 8 and 12?
4.
QUESTION 2
What is the LCM of 3 and 5?
15.
QUESTION 3
What is the difference between a factor and a multiple?
A factor divides evenly into a number; a multiple is the result of multiplying a number by an integer.

Going deeper? Prime factorization.

Have students find GCF and LCM using prime factorization — breaking each number into its prime factors. A printable GCF/LCM sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 GCF & LCMFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 GCF & LCMQuiz
Score: 0
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ GCF & LCMPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: common, distributive property, divide evenly, factor, GCF, LCM, multiple, prime factorization
  1. no remainder
  2. greatest common factor
  3. a number that divides evenly
  4. shared by both
  5. a number as a product of primes
  6. least common multiple
  7. a product of a number
  8. a(b+c)=ab+ac

Part B · Show what you learned

  1. What is the GCF of 8 and 12?
  2. What is the LCM of 3 and 5?
  3. What is the difference between a factor and a multiple?
Answer key — Part A: 1) divide evenly · 2) GCF · 3) factor · 4) common · 5) prime factorization · 6) LCM · 7) multiple · 8) distributive property
Part B: 1) 4. 2) 15. 3) A factor divides evenly into a number; a multiple is the result of multiplying a number by an integer.