Factors, Multiples, GCF & LCM

Grade 5 · Mathematics

Semester 1 | Period 1 | Week 4

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Subject: Mathematics

Semester: 1

Period: 1

Week: 4

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 4
Lesson Duration: 45 minutes
Week & Period: Week 4, Period 1
Topic: Factors, Multiples, GCF & LCM
Sub-topic: Word Problems with GCF and LCM

Learning Objectives
By the end of the lesson, students should be able to:

  1. Define factors and multiples.
  2. Find GCF and LCM using listing and prime factorization.
  3. Solve word problems involving GCF and LCM.

Previous Knowledge
Students already know multiplication and prime numbers.

Instructional Materials
Charts, counters, number cards

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: “What are the factors of 12?” “What are the multiples of 3?”

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

 Full Definitions & Explanations

  1. Factor
    A factor is a number that divides another number exactly, leaving no remainder.
    • ✅ Example: Factors of 12 are 1, 2, 3, 4, 6, 12
    • ❌ 5 is not a factor of 12 because 12 ÷ 5 = 2.4 (not a whole number)
  2. Multiple
    A multiple is the result of multiplying a number by whole numbers (1, 2, 3, 4…).
    • ✅ Example: Multiples of 5 are 5, 10, 15, 20, 25, 30…
  3. Greatest Common Factor (GCF)
    The largest number that divides two or more numbers exactly.
    • ✅ Example: GCF of 24 and 36 = 12
  4. Least Common Multiple (LCM)
    The smallest number that is a multiple of two or more numbers.
    • ✅ Example: LCM of 6 and 8 = 24

 

🧠 Conceptual Notes

  • GCF is useful in sharing items equally or reducing fractions.
  • LCM is useful in scheduling or synchronizing events.
  • Factors are finite, multiples are infinite.

 

🔢 More Examples

✅ Factors:

  • Factors of 18 = 1, 2, 3, 6, 9, 18
  • Factors of 20 = 1, 2, 4, 5, 10, 20

✅ Multiples:

  • Multiples of 4 = 4, 8, 12, 16, 20, 24…
  • Multiples of 6 = 6, 12, 18, 24, 30, 36…

🧩 GCF Examples:

  1. GCF of 12 and 18
    • Factors of 12: 1, 2, 3, 4, 6, 12
    • Factors of 18: 1, 2, 3, 6, 9, 18
    • Common factors = 1, 2, 3, 6 → GCF = 6
  2. GCF of 30 and 45
    • Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
    • Factors of 45: 1, 3, 5, 9, 15, 45
    • GCF = 15

🔄 LCM Examples:

  1. LCM of 4 and 6
    • Multiples of 4: 4, 8, 12, 16…
    • Multiples of 6: 6, 12, 18…
    • Common multiple = 12 → LCM = 12
  2. LCM of 5 and 10
    • Multiples of 5: 5, 10, 15, 20…
    • Multiples of 10: 10, 20, 30…
    • LCM = 10

 

📝 Word Problems (Expanded)

  1. Synchronization (LCM):
    Two friends clap every 6 sec and 8 sec. When will they clap together?
    → LCM of 6 and 8 = 24 seconds
  2. Sharing Items (GCF):
    A farmer has 30 mangoes and 45 oranges. What is the largest number of equal baskets he can make without cutting any fruit?
    → GCF of 30 and 45 = 15 baskets
  3. Cooking Example (LCM):
    Rice takes 12 mins to cook, beans takes 16 mins. After how many minutes will both finish cooking at the same time?
    → LCM of 12 and 16 = 48 minutes
  4. Ribbons Example (GCF):
    You have ribbons of 18 cm and 24 cm. What is the longest length you can cut from both without any leftover?
    → GCF of 18 and 24 = 6 cm

 

👩🏽‍🏫 Learners’ Activities (Expanded)

  1. Card Sorting Game (GCF & LCM):
    • Learners are given number cards.
    • In groups, they pick 2 cards and find:
      • All factors (to find GCF)
      • First 5 multiples (to find LCM)
  1. Number Ladder Race (GCF):
    • Teams race to write all factors of given numbers on the board and circle the greatest common factor.
  2. Multiple Relay (LCM):
    • In relay form, learners write the multiples of given pairs and underline the least common multiple.
  3. Word Problem Challenge:
    • Learners work in pairs to solve LCM and GCF word problems using listing or prime factorization methods.

 

✅ Assessment Checks

  1. Quick Oral Quiz:
    • "What are the factors of 16?"
    • "What is the LCM of 3 and 5?"
    • "Find the GCF of 14 and 28."
  2. Mini Worksheet:

Number Pair

GCF

LCM

12 and 15

    

9 and 6

    

10 and 25

    
  1. True or False?
    • "24 is a multiple of 6." ✅
    • "15 is a factor of 40." ❌
    • "The GCF of 9 and 27 is 9." ✅
  2. Exit Ticket:
    Each learner writes:
    • One factor of 36
    • One multiple of 7
    • A GCF of two numbers of their choice
    • An LCM of any two numbers

 

📎 Notes (Expanded & Detailed)

  • GCF (Also called HCF) is commonly used in:
    • Simplifying fractions
    • Finding how to equally divide items
  • LCM is commonly used in:
    • Scheduling activities
    • Solving problems involving repeating events
  • Methods to Find GCF & LCM:
    • Listing Method: List all factors/multiples and pick the correct one.
    • Prime Factorization: Break each number into prime factors using factor trees.

 

🧮 Optional Extension Activity

Prime Factorization Trees:

  • Learners create prime factor trees for 36 and 60.
  • Then they circle common factors to find the GCF.
  • Multiply all common prime factors to get the GCF.
  • Multiply all prime factors from both numbers (taking highest powers) to get LCM.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews how to find GCF and LCM.

Evaluation Method (Expanded):
Exit slip/quiz: Find LCM of 4 and 10; Find GCF of 20 and 30.

Assignment (Expanded):
Textbook problems on GCF and LCM.

Follow-up Activity:
Students create their own word problems using GCF and LCM.

Differentiation / Inclusive Strategies
Use manipulatives for weaker learners.

Teacher’s Reflection (After Class)
• What worked well? ___________________________________________
• What needs improvement? ____________________________________
• Students’ engagement level: ☑ High ☑ Medium ☑ Low