Overview

This 60-minute lesson introduces Year 9 students to the concept of the Lowest Common Multiple (LCM), focusing on understanding what LCM is, methods to find it (listing multiples and prime factorisation), and applying their knowledge through practical problems. The lesson fully aligns with the National Curriculum for England: Key Stage 3 (Years 7-9), particularly the programme of study on number - prime factors, powers, roots, and surds.

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National Curriculum links

• Arithmetic and Number: Pupils should be taught to:
  • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
  • Identify common factors, common multiples and prime numbers.
• Mathematical Reasoning and Problem Solving:
  • Apply knowledge of primes, factors and multiples.
  • Solve problems involving multiples and factors, scales, etc.

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Learning Objectives

By the end of this lesson, students will:

• Understand the concept of LCM and its importance.
• Find LCM for pairs or sets of numbers by listing multiples.
• Find LCM using prime factorisation.
• Solve word problems involving LCM in real-life contexts.
• Collaborate effectively during group tasks and demonstrate independent problem-solving skills.

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Resources Needed

• Whiteboard and markers
• PowerPoint/slideshow with worked examples and visual aids
• Student handouts with practice problems and prime factor trees templates
• Mini whiteboards for quick formative assessment
• Bingo cards with multiples for starter activity
• Laptops/tablets (optional for interactive group tasks)
• Timer

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Lesson Outline

Starter (10 minutes) – Multiples Bingo

Purpose: Activate prior knowledge; engage students immediately.

• Each student receives a bingo card filled with multiples of certain numbers (e.g. 3, 4, 5, 6, 8).
• Teacher calls out random numbers, and students mark multiples of these numbers on their cards.
• Discuss what multiples are briefly and relate to factors.
• Quick prompt: “If 12 is a multiple of 3 and 4, what do you think the lowest common multiple means?”

Assessment: Monitor participation, select 2-3 students to share thoughts.

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Introduction & Direct Teaching (15 minutes)

Topic: What is LCM?

• Begin with definition: The lowest common multiple of two or more numbers is the smallest number (other than zero) that is a multiple of all the numbers.
• Use a visual: number lines showing multiples of two numbers and highlighting intersection points.
• Worked example on whiteboard: LCM of 4 and 6 by listing multiples.
• Transition: Explain when listing multiples becomes inefficient with larger numbers – introduce prime factorisation method as an efficient alternative.
• Explain prime factorisation briefly with an example (e.g. 12 = 2² × 3, 18 = 2 × 3²).
• Demonstrate finding LCM using prime factors by taking highest powers of each prime.
• Show comparison of both methods with one example.

Curriculum Link: Develops fluency and reasoning within Number - multiples and factors (Number objectives for Year 9).

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Group Activity (15 minutes) – Prime Factor Tree Challenge

• Students organize into groups of 4-5.
• Each group receives 3 pairs of numbers (increasing difficulty, e.g., 8 & 12, 15 & 18, 24 & 32).
• Use prime factor trees to find the LCM of each pair, explaining steps collaboratively.
• Groups record their answers and methods.
• Teacher circulates, probing student understanding and clarifying misconceptions (e.g., confusing HCF and LCM).

Extension: For fast groups, challenge them to find LCM of three numbers or explain real-world scenarios when to use LCM.

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Independent Practice (15 minutes) – Diverse LCM Problems

• Students complete worksheet with:
  • Listing multiples to find LCM (simpler numbers).
  • Using prime factorisation (larger or multiple numbers).
  • Word problems involving LCM (e.g., scheduling events that recur at different intervals).
• Encourage students to write out prime factor trees where needed, showing working.
• Teachers use mini whiteboards for quick checks of answers during this session.

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Plenary & Assessment (5 minutes) – Exit Ticket & Reflect

• Each student writes an “exit ticket” response to the question:
  “Explain in your own words what the LCM is and write one method to find it.”
• Collect exit tickets for quick formative assessment of understanding.
• Quick Q&A to clarify any final confusions.
• Highlight how understanding LCM links to wider topics (fractions, ratios, algebra).

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Differentiation & SEND Considerations

• Provide prime factor trees partially completed for scaffolding.
• Use visual aids and manipulatives (like counters) for those who benefit from concrete examples.
• Pair SEND students with supportive peers during group work.
• Use clear, concise language and pre-teach vocabulary such as 'multiple', 'factor', 'prime number'.

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Assessment Ideas

• Formative: Observation during group work, bingo participation, mini whiteboard checks, exit tickets.
• Summative (optional homework or next lesson): Worksheet combining LCM and HCF problems with problem-solving context questions.
• Stretch task suggestion: Investigate LCM for more than two numbers; relate LCM to real-life applications (e.g., synchronising traffic light cycles).

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Summary

This lesson plan delivers an engaging, clearly scaffolded approach to mastering LCM tailored to Year 9, firmly rooted in the statutory National Curriculum requirements for England. By combining interactive warm-ups, direct instruction, collaborative learning, and individual consolidation with measurable assessment points, it caters to diverse learning needs and builds a strong number foundation pivotal for future mathematical success.