Courseversity

Lesson

Least common multiple

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-NUM-U01-L0635–45 min

You will learn

  • List multiples.
  • Find the LCM.
  • Solve timing problems.
  • Link LCM to fractions.

Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.

Student lesson

Words to know

common multiple
A multiple of both.
LCM
Least common multiple.
multiple
Times-table number.
interval
Time between events.

1. Discover: two buses

One bus leaves every 4 minutes and another every 6. When do they leave together again?

2. Understand: least common multiple

  • Multiples of 4: 4, 8, 12, 16, 20, 24.
  • Multiples of 6: 6, 12, 18, 24.
  • The LCM of 4 and 6 is 12, so after 12 minutes.
  • LCM of 6 and 8 is 24; LCM of 3 and 5 is 15.
Remember: List multiples, pick the first shared.

3. Explore: lcm

You need paper.

  1. List multiples of each.
  2. Find the first match.
  3. Name the LCM.
  4. Use it in the story.
Think about it: what did you notice?

12 minutes.

4. Practise

Guided practice

Question 1. LCM of 4 and 6?

12.

Question 2. LCM of 6 and 8?

24.

Question 3. LCM of 3 and 5?

15.

Independent practice

  1. LCM of 2 and 7
  2. LCM of 6 and 9
  3. LCM of 10 and 15
  4. LCM of 4 and 8
  5. Buses at 4 and 6 minutes: second time together

Answers are in the answer key below. Try first, then check.

5. Apply: everyday mathematics

Two lights flash every 4 s and every 6 s. When do they flash together?

Show a sample answer

Every 12 seconds.

6. Common mistake

Mistake: Giving the product 24 for 4 and 6.
Fix: Check for a smaller match, 12.

7. Check and master

Answer all questions. You will see feedback after each one.

1. LCM of 4 and 6:

2. LCM of 2 and 7:

3. LCM of 6 and 9:

4. LCM of 10 and 15:

5. LCM of 4 and 8:

Challenge. Buses at 4 and 6 minutes meet again at:

Your result appears here after you answer every question.

8. Key takeaways

  • List multiples.
  • First shared is the LCM.
  • LCM solves timing problems.

9. Next lesson

Next lesson: Introduction to integers. Keep going with the next idea in this course.

Printable worksheet

  1. LCM of 2 and 7
  2. LCM of 6 and 9
  3. LCM of 10 and 15
  4. LCM of 4 and 8
  5. Second time buses meet (4 and 6)

Homework

Find the LCM of 12 and 15.

Answer key and marking scheme

Question Expected response Marks
LCM of 2 and 7 14 2
LCM of 6 and 9 18 2
LCM of 10 and 15 30 2
LCM of 4 and 8 8 2
Second time buses meet (4 and 6) 24 minutes 2
Total 10

Practice answers: Worksheet: 1 14; 2 18; 3 30; 4 8; 5 24 minutes.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 List multiples Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Find the LCM Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Solve timing problems Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Link LCM to fractions Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Giving the product 24 for 4 and 6. Check for a smaller match, 12.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Multiples of 4 and 6.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: list multiples; find the LCM; solve timing problems; link LCM to fractions.

Prerequisite knowledge. Lesson 3.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 35–45 minutes.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Giving the product 24 for 4 and 6. Check for a smaller match, 12.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Multiples of 4 and 6. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.

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