Finding LCM & GCD

Curriculum Standards

Grade Level: 5th Grade
Curriculum Area: Number and Operations in Base Ten (Common Core Standard 5.NBT.B.6)
Focus: Understand Least Common Multiple (LCM) and Greatest Common Divisor (GCD) with simple examples.

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Lesson Objective

By the end of this lesson, students will be able to:

1. Understand the basic concepts of LCM and GCD.
2. Find the LCM and GCD of two simple numbers.
3. Apply their understanding through an interactive group activity.

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Materials Needed

• Whiteboard
• Markers (different colors for clear demonstration)
• Preprinted number cards (1–20, random order)
• Mini whiteboards or scratch paper for students
• A timer

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Warm-Up (1 Minute)

Mental Math Game: "Multiples Magic"

1. Teacher will ask the class to call out the first 3 multiples of 2 (e.g., 2, 4, 6).
2. Repeat with 3 (e.g., 3, 6, 9).
3. Quick quiz: "Can any two numbers share a multiple?" (E.g., 2 and 3 both have 6 as a multiple).
   • Purpose: Activate prior knowledge of multiples.

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Direct Instruction (2 Minutes)

Step 1: What is LCM?

• Definition: “The Least Common Multiple (LCM) is the smallest multiple that two numbers share.”
• Example:
  • Let’s find the LCM of 2 and 3.
  • Write the multiples of each number on the board:
    • 2: 2, 4, 6, 8, 10...
    • 3: 3, 6, 9, 12...
  • Circle common multiples: 6, 12...
  • The least common one is 6, so LCM(2,3) = 6.

Step 2: What is GCD?

• Definition: “The Greatest Common Divisor (GCD) is the largest number that divides two numbers evenly.”
• Example:
  • Find the GCD of 12 and 16.
  • List the factors of each number:
    • 12: 1, 2, 3, 4, 6, 12
    • 16: 1, 2, 4, 8, 16
  • Circle common factors: 1, 2, 4.
  • The greatest one is 4, so GCD(12,16) = 4.

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Activity (2 Minutes)

Pair-Up Game: “LCM & GCD Detectives”

1. Divide the Class: Students pair up (15 pairs in total). Each pair gets 2 preprinted number cards (e.g., 6 and 9).
2. Step 1 - Find the LCM: Using scratch paper or mini whiteboards, students list multiples of their two numbers and circle the LCM.
3. Step 2 - Find the GCD: Students list the factors of their two numbers and circle the GCD.
4. Teacher walks around offering encouragement and checks their work.

Example Pair Activity:

• Example cards: 6 and 9
  • LCM: Multiples of 6 (6, 12, 18) and 9 (9, 18, 27). LCM = 18.
  • GCD: Factors of 6 (1, 2, 3, 6) and 9 (1, 3, 9). GCD = 3.

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Wrap-Up (1 Minute)

1. Quick class quiz: Teacher writes two numbers (like 8 and 12) on the board and asks:
   • “What’s the LCM?”
   • “What’s the GCD?”
   • Call on volunteers to share answers.
2. Summarize key learning points:
   • LCM is the least shared multiple.
   • GCD is the greatest shared factor.

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Teaching Tip

Excite the students by framing them as "Math Detectives" searching for patterns between numbers. Use a celebratory cheer for correct answers, like “You cracked the case!”

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This lesson plan ensures engagement and understanding within a 5-minute time frame. Teachers can extend the activity for deeper exploration if needed.