Free Grade 3 Introducing Multiples Lessons
Free Grade 3 lessons for Introducing Multiples: 12 real questions with a full answer key and worked solutions. Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
Free
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing multiples
Identify introducing multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing multiples
Explain introducing multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing multiples
Calculate introducing multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing multiples
Compare introducing multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introducing Multiples works
Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.List all the factors of 30.[1]
- 2.List all the factors of 28.[1]
- 3.List all the factors of 12.[1]
- 4.List all the factors of 40.[1]
- 5.Find the highest common factor (HCF) of 10 and 30.[2]
- 6.Find the highest common factor (HCF) of 16 and 56.[2]
- 7.Find the highest common factor (HCF) of 54 and 54.[2]
- 8.Find the highest common factor (HCF) of 27 and 18.[2]
- 9.Find the lowest common multiple (LCM) of 14 and 12.[3]
- 10.Find the lowest common multiple (LCM) of 40 and 16.[3]
- 11.Find the lowest common multiple (LCM) of 6 and 8.[3]
- 12.Find the lowest common multiple (LCM) of 25 and 15.[3]
Show answers and working
1. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
2. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
3. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
4. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
5. 10
List factors of 10 and 30. The largest factor they share is 10.
6. 8
List factors of 16 and 56. The largest factor they share is 8.
7. 54
List factors of 54 and 54. The largest factor they share is 54.
8. 9
List factors of 27 and 18. The largest factor they share is 9.
9. 84
HCF(14, 12) = 2. LCM = 14 × 12 ÷ 2 = 84.
10. 80
HCF(40, 16) = 8. LCM = 40 × 16 ÷ 8 = 80.
11. 24
HCF(6, 8) = 2. LCM = 6 × 8 ÷ 2 = 24.
12. 75
HCF(25, 15) = 5. LCM = 25 × 15 ÷ 5 = 75.
Worked examples
List all the factors of 20.
- Find factor pairs that multiply to 20.
- 1 × 20
- 2 × 10
- 4 × 5
- Answer: 1, 2, 4, 5, 10, 20
Find the highest common factor (HCF) of 45 and 27.
- List factors of 45 and 27.
- The largest factor they share is 9.
- Answer: 9
Find the lowest common multiple (LCM) of 32 and 16.
- HCF(32, 16) = 16.
- LCM = 32 × 16 ÷ 16 = 32.
- Answer: 32
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Mixes up factors and multiples.
Correction: Factors are Few (they fit inside), multiples are Many (they go on forever).
Misses factor pairs.
Correction: Work through 1, 2, 3… in order until the pairs meet.
Teacher tips
- · Use factor rainbows to show pairs.
Parent tips
- · Ask how many ways 24 sweets can be put into equal bags.
Real-life applications
- · Arranging chairs in equal rows, syncing bus timetables (LCM).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Introducing Multiples lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Factors. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Multiples?
- Move on to Working with Multiples, Multiples in Context, Factors, Prime Numbers, which build directly on this idea.
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