What Are Multiples?
A multiple of a number is what you get when you multiply that number by any whole number (1, 2, 3, 4, ...). Multiples are like the number's times table — they go on forever.
Formal Definition
M is a multiple of N if M = N × k for some positive whole number k.
Examples
| Number | First 8 Multiples |
|---|---|
| 3 | 3, 6, 9, 12, 15, 18, 21, 24 |
| 7 | 7, 14, 21, 28, 35, 42, 49, 56 |
| 12 | 12, 24, 36, 48, 60, 72, 84, 96 |
| 0.5 | 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4 |
Key Properties of Multiples
- The first multiple of any number is the number itself (n × 1 = n).
- Multiples are always equal to or greater than the number.
- There are infinitely many multiples of any number.
- Every number is a multiple of 1.
- Zero is technically a multiple of every number (n × 0 = 0) — but is usually excluded from lists.
Multiples vs Factors – Side by Side
| Property | Factors | Multiples |
|---|---|---|
| Relationship | Divide INTO the number | Number divides INTO them |
| Size | ≤ the number | ≥ the number |
| Count | Finite | Infinite |
| Example (6) | 1, 2, 3, 6 | 6, 12, 18, 24... |
Multiples in Real Life
- Clocks: Minutes are multiples of 1; quarter hours are multiples of 15.
- Music: Beats repeat in multiples of the time signature.
- Packing: Boxes of 12 — stock levels are multiples of 12.
Key Takeaways
- Multiples = the number × 1, 2, 3, 4... (times table extended infinitely).
- A number is a multiple of its own factors.
- Multiples are always ≥ the original number (excluding 0).
- Finding common multiples leads to the LCM.
Practice Questions
- List the first 6 multiples of 8.
- Is 45 a multiple of 9? Show why.
- List the first 5 multiples of 11.
- Which numbers between 50 and 70 are multiples of 7?
- True or false: every even number is a multiple of 2.