Home›Lesson Plans›Mathematics›The Number System · Grade 6

GCF and LCM

Sixth graders learn to find the greatest common factor and least common multiple of two numbers, telling factors from multiples, and check what they know.

Grade 6GCF and LCM50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Assign or share this lesson
Share to Google Classroom Share to Microsoft Teams

Copy link works with Canvas, Schoology, Moodle and any other LMS — paste it in as a resource or assignment.

Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Tell factors from multiples.
  • ✓Find the GCF.
  • ✓Find the LCM.
  • ✓Pick which to use.
Essential Question

Two numbers can share factors and share multiples. What are the biggest shared factor and the smallest shared multiple called, and when do you use each?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

GCF and LCM Check

Project this and answer each question about greatest common factor and least common multiple — read the explanation after each one.

🧮 Check what you know about GCF and LCMTry it
Answer each question about greatest common factor and least common multiple.
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

Hook — Shared Numbers

5 min

Two numbers can share factors and share multiples. The biggest shared factor and the smallest shared multiple each have a special name and a real use. What are they?

👩‍🏫 Teacher Moves

  • Show 12 and 18.
  • Ask what they share.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — GCF and LCM Check

12 min

Students answer questions about GCF and LCM.

👩‍🏫 Teacher Moves

  • Send students to the GCF and LCM Check.
  • Answer each question.
  • Read the why.

🎒 Student Actions

  • Answer.
  • Check.
  • Read it.
3

Modify — List and Find

13 min

Students find a GCF or LCM.

👩‍🏫 Teacher Moves

  • Take two numbers.
  • List factors or multiples.
  • Circle the GCF or LCM.

🎒 Student Actions

  • Take.
  • List.
  • Circle.
4

Create — Real Use

15 min

Students apply GCF or LCM.

👩‍🏫 Teacher Moves

  • Write a sharing problem (GCF) or a repeating-event problem (LCM).
  • Solve it.
  • Say which you used.

🎒 Student Actions

  • Write.
  • Solve.
  • Say.
5

Reflect — Factors and Multiples

5 min

Students reflect on GCF and LCM.

👩‍🏫 Teacher Moves

  • What is the GCF of two numbers?
  • How is a multiple different from a factor?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say 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.B.4

Find the greatest common factor of two whole numbers less than or equal to 100.

CCSS
6.NS.B.4

Find the least common multiple of two whole numbers less than or equal to 12.

CCSS
4.OA.B.4

Find all factor pairs for a whole number and recognize multiples.

CCSS
MP.7

Look for and make use of structure.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Factor/multiple lists.
  • Sentence frame: “The GCF / LCM of ___ and ___ is ___ .”
  • Answer one question at a time.

Support & Access

IEP / 504
  • Start by listing factors and multiples.
  • Use small numbers first.
  • Circle shared values together.

Stretch & Extend

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

What to gather

  • 📽️Projector / board
  • 🧮Factor/multiple charts
  • 💻GCF and LCM Check
  • 🖼️Number cards
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

factora number that divides another number evenlymultiplethe product of a number and a whole numbergreatest common factorthe largest factor two numbers share (GCF)least common multiplethe smallest multiple two numbers share (LCM)commonshared by two or more numbersprime factorizationwriting a number as a product of primesdivide evenlyto divide with no remainderwhole numbera non-negative number with no fraction part
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 two numbers?
The largest factor that divides both numbers evenly.
QUESTION 2
How is a multiple different from a factor?
A factor divides a number; a multiple is the number times a whole number.
QUESTION 3
Find the GCF of 8 and 12.
4, the largest factor shared by 8 and 12.

Create: a real use.

Have students write a sharing problem (GCF) or a repeating-event problem (LCM), solve it, and say which they used, so the ideas connect to real situations. A printable GCF-and-LCM worksheet is in the Mathematics 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 and LCMFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

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

📝 GCF and LCMQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

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 and LCMPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: common, divide evenly, factor, greatest common factor, least common multiple, multiple, prime factorization, whole number
  1. the smallest multiple two numbers share (LCM)
  2. shared by two or more numbers
  3. to divide with no remainder
  4. a non-negative number with no fraction part
  5. the largest factor two numbers share (GCF)
  6. writing a number as a product of primes
  7. a number that divides another number evenly
  8. the product of a number and a whole number

Part B · Show what you learned

  1. What is the GCF of two numbers?
  2. How is a multiple different from a factor?
  3. Find the GCF of 8 and 12.
Answer key — Part A: 1) least common multiple · 2) common · 3) divide evenly · 4) whole number · 5) greatest common factor · 6) prime factorization · 7) factor · 8) multiple
Part B: 1) The largest factor that divides both numbers evenly. 2) A factor divides a number; a multiple is the number times a whole number. 3) 4, the largest factor shared by 8 and 12.