The idea, step by step
Count repeated groups
A multiple is the total made by a whole number of equal groups. One group of six gives six, two groups give twelve and three groups give eighteen. Continue adding six to list 6, 12, 18, 24, 30 and so on.
Zero is also a multiple of every whole number because zero groups give zero. When a question asks for the first positive multiples, start with one group rather than zero.
| Number of groups | Calculation | Total |
|---|---|---|
| 1 | 1 × 6 | 6 |
| 2 | 2 × 6 | 12 |
| 3 | 3 × 6 | 18 |
| 4 | 4 × 6 | 24 |
Find totals shared by two patterns
A common multiple belongs to both lists. Multiples of four begin 4, 8, 12, 16, 20, 24. Multiples of six begin 6, 12, 18, 24. Twelve and twenty-four appear in both lists.
A number has only a limited number of positive factors, but its multiples keep going. For example, the factors of six stop at six, while its multiples include twelve, eighteen and much larger numbers.
A common trap
Calling 3 a multiple of 12 because 3 divides 12.
Instead: Three is a factor of twelve. Multiples of twelve are made by multiplying twelve by whole numbers, such as 12, 24 and 36.
See the thinking
Make a multiple list
Write the first five positive multiples of 8.
- Start with one group: 8.
- Add eight each time, or multiply eight by 2, 3, 4 and 5.
- Stop after five positive totals.
Match two repeating alarms
One alarm sounds every 4 minutes and another every 6 minutes. They sound together now. After how many minutes will they next sound together?
- List positive multiples of four: 4, 8, 12, ...
- List positive multiples of six: 6, 12, ...
- The first positive time in both lists is twelve.
Check your understanding
What is the sixth positive multiple of 7?
Show answer
42.
Six groups of seven give 6 × 7 = 42.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- Write the first four positive multiples of 9.1 mark
- Write the next two numbers: 5, 10, 15, 20, __, __.1 mark
- Is 54 a multiple of 6? Give a multiplication fact.1 mark
- List all positive multiples of 8 that are less than 40.2 marks
- Find the positive common multiples of 3 and 4 that are at most 30.2 marks
- A teacher needs the same number of pencils packed in groups of five or groups of six, with none left over. What is the smallest possible positive total?3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write the first four positive multiples of 9.1 mark
Multiply nine by one, two, three and four.
9, 18, 27, 36. - Write the next two numbers: 5, 10, 15, 20, __, __.1 mark
Add five at each step.
25, 30. - Is 54 a multiple of 6? Give a multiplication fact.1 mark
A whole number of groups of six makes fifty-four.
Yes: 6 × 9 = 54. - List all positive multiples of 8 that are less than 40.2 marks
The next multiple is forty, but it is not less than forty.
8, 16, 24, 32. - Find the positive common multiples of 3 and 4 that are at most 30.2 marks
Multiples of four are 4, 8, 12, 16, 20, 24, 28.
Twelve and twenty-four are also multiples of three.
12 and 24. - A teacher needs the same number of pencils packed in groups of five or groups of six, with none left over. What is the smallest possible positive total?3 marks
List multiples of five and six.
Thirty is the first positive total shared by the lists.
30 pencils.
Curriculum reference & lesson scope
Australian Curriculum v9.0; SA Curriculum Mathematics 2026
Factor pairs; multiples; divisibility; factor/divisibility algorithms.
Official curriculum source ↗