You will learn
- List multiples of a number.
- Tell if a number is a multiple.
- Find common multiples.
- Tell factors from multiples.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Multiples come from a times table.
- Skip count to list them.
- A common multiple belongs to both numbers.
- The least common multiple is the smallest.
Words to know
A number in a times table.
A multiple shared by two numbers.
Count by equal jumps.
Exactly divisible.
1. Discover: buses
One bus comes every 6 minutes and another every 4. When will they arrive together?
2. Understand: multiples
A multiple of a number is in its times table.
- Multiples of 6: 6, 12, 18, 24, 30, 36 …
- Multiples of 4: 4, 8, 12, 16, 20, 24 …
- Common multiples of 4 and 6: 12, 24, 36 … The least is 12.
Factors are small and finite; multiples go on forever. 18 is a multiple of 6 because 18 ÷ 6 = 3.
Idea 1: List
Multiples of 7: 7, 14, 21, 28, 35 and so on. The third multiple of 9 is 27.
Idea 2: Test
Is 35 a multiple of 5? 5 × 7 = 35, so yes. Is 20 a multiple of 6? 6, 12, 18, 24: no.
Idea 3: Common
Multiples of 3: 3, 6, 9, 12, 15. Multiples of 5: 5, 10, 15. The first common multiple is 15.
Why least? The least common multiple is the first one both lists share.
3. Worked examples
Example 1 (I show you): List
First five multiples of 7
- Skip count in 7s.
Answer: 7, 14, 21, 28, 35
Example 2 (We do it together): Common
First common multiple of 3 and 5
- List both until a match.
Answer: 15
Example 3 (You try): Test
Is 20 a multiple of 6?
Show the steps and answer
- 6, 12, 18, 24.
Answer: No
Did you know?
Multiples go on forever, but factors stop.
Why this matters
Common multiples help with timetables, fractions and patterns.
4. Explore: list and match
You need paper.
- List 6 multiples of 4.
- List 6 multiples of 6.
- Circle the numbers in both.
- Name the least common one.
Think about it: what did you notice?
12.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The multiples of ___ are ___.
- ___ is a multiple of ___ because ___.
- A common multiple of ___ and ___ is ___.
- The least common multiple is ___.
Guided practice
Question 1. Multiples of 6?
6, 12, 18, 24, 30.
Question 2. Least common multiple of 4 and 6?
12.
Question 3. Is 18 a multiple of 6?
Yes.
Independent practice
Level 1: Start
- First five multiples of 7
- Is 35 a multiple of 5? (yes/no)
- First common multiple of 3 and 5
- Is 20 a multiple of 6? (yes/no)
- Third multiple of 9
Level 2: Grow
- First four multiples of 6
- Is 56 a multiple of 8?
- First common multiple of 2 and 7
Level 3: Stretch
- Least common multiple of 6 and 9
- The tenth multiple of 12
- Ben says 12 is a multiple of 8 because 8 + 4 = 12. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Buses leave every 6 and 4 minutes together at 8:00. When next together?
Show a sample answer
8:12.
Another one. One bus leaves every 6 minutes and another every 8 minutes. They leave together now. When do they next leave together?
Show a sample answer
The least common multiple of 6 and 8 is 24, so after 24 minutes.
7. Common mistakes
Fix: Factors divide; multiples are found by multiplying.
Fix: Factors divide; multiples come from the times table.
Fix: Compare the lists in order.
8. Lesson summary and revision card
- I can list multiples.
- I can tell if a number is a multiple.
- I can find common multiples.
- I can tell factors from multiples.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Multiples are in times tables.
- Common multiples are shared.
- Multiples go on forever.
11. Next lesson
Next lesson: Prime numbers. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Write the first five multiples of 7. [2 marks]
- Is 35 a multiple of 5? Explain. [2 marks]
- Find the first common multiple of 3 and 5. [3 marks]
- Is 20 a multiple of 6? Explain. [2 marks]
- Ana says the third multiple of 9 is 18. Is she right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- Skip count in 7s [1]; 7, 14, 21, 28, 35 [1]
- 5 × 7 = 35 [1]; yes [1]
- 3, 6, 9, 12, 15 [1]; 5, 10, 15 [1]; 15 [1]
- 6, 12, 18, 24 [1]; no [1]
- No [1]. 9, 18, 27 [1]. It is 27 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- First five multiples of 7
- Is 35 a multiple of 5? (yes/no)
- First common multiple of 3 and 5
- Is 20 a multiple of 6? (yes/no)
- Third multiple of 9
- A multiple of 6 is
- The least common multiple of 4 and 6 is
- First five multiples of 7:
- Is 35 a multiple of 5?
- First common multiple of 3 and 5:
Homework
List multiples of 3 and 5 up to 60 and circle the common ones.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| First five multiples of 7 | 7, 14, 21, 28, 35 | 2 |
| Is 35 a multiple of 5? (yes/no) | yes | 2 |
| First common multiple of 3 and 5 | 15 | 2 |
| Is 20 a multiple of 6? (yes/no) | no | 2 |
| Third multiple of 9 | 27 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 7, 14, 21, 28, 35; 2 yes; 3 15; 4 no; 5 27.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 24; 7 12; 8 7, 14, 21, 28, 35; 9 yes; 10 15.
Independent practice answers. Level 1: 1 7, 14, 21, 28, 35; 2 yes; 3 15; 4 no; 5 27. Level 2: 1 6, 12, 18, 24; 2 yes; 3 14. Level 3: 1 18; 2 120; 3 Multiples of 8 are 8, 16, 24, so 12 is not one..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 List multiples of a number | 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 Tell if a number is a multiple | 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 Find common 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 |
| O4 Tell factors from 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Mixing up factors and multiples. Factors divide; multiples are found by multiplying.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Skip count on a number line.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child lists multiples and finds common multiples. You do not need to be good at mathematics to help.
- Skip count in the car.
- Ask: is it in the times table?
- Use timetables to find common multiples.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: list multiples of a number; tell if a number is a multiple; find common multiples; tell factors from multiples.
Prerequisite knowledge. Lessons 1 and 2, times tables.
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. 45–60 minutes. It can be split into two shorter sessions.
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.
Key questions. Is it in the times table? What do both lists share?
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. Mixing up factors and multiples. Factors divide; multiples are found by multiplying.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Skip count on a number line. 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.
Research used to shape this lesson. Common Core 4.OA.B.4 and 6.NS.B.4; Cambridge Primary Mathematics Stage 4 and 5 (multiples). These sources informed the lesson; no official alignment is claimed.