Understand the idea.
Count repeated groups
A multiple is made by taking a whole number of equal groups. Groups of give , and . Each new group adds another , so the sequence continues without an upper limit.
Zero groups give , so zero is also a multiple of . Read the wording: “first five positive multiples” starts at one group and excludes zero. Count how many totals you list, not how many additions you make.
| 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 appears in the multiples of both numbers. For and , the first positive shared total is : it can be made as three groups of four or two groups of six.
Factors and multiples point in different directions. Factors divide the original number exactly and cannot exceed a positive target. Multiples are totals made from that number, and keep growing. A repeating-event question usually asks for a shared multiple, not a shared factor.
See the method in action.
Make a multiple list
Write the first five positive multiples of 8.
Worked solution
- 1
Begin with one group of eight.
The word positive means the list starts above zero.
- 2
Calculate the next four group totals.
Each extra group increases the total by 8.
- 3
Check that five positive multiples are listed.
The list contains the totals for one through five groups.
8, 16, 24, 32, 40.
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?
Worked solution
- 1
List the first alarm times after now.
An alarm every 4 minutes sounds at positive multiples of 4.
- 2
List the second alarm times after now.
An alarm every 6 minutes sounds at positive multiples of 6.
- 3
Find the first positive time in both lists.
12 minutes is shared; none of the earlier positive times match.
After 12 minutes.
Try it yourself.
Check your understanding
What is the sixth positive multiple of 7?
Show answer & reasoning
42.
The sixth positive multiple counts six groups: . Starting with zero would count the wrong position.
Keep practising
6 worksheet questions · 10 marks
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: . - 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 ↗