What is a multiple in math?
A multiple of a number is the result of multiplying that number by any whole number. The multiples of 4 are 4, 8, 12, 16, and so on, continuing without end. Every number is a multiple of itself and of 1. To test a number, divide: if the remainder is 0, it is a multiple.
Multiple in a picture
Formal definition and notation
A whole number m is a multiple of a whole number n if m = n × k for some whole number k. When n ≠ 0, this is the same as saying n divides m with remainder 0, so n is a factor of m. Most school lists use k = 1, 2, 3, …, so they start with n itself and leave out 0. A number that is a multiple of two numbers is a common multiple; the smallest positive one is the least common multiple.
| Symbol | Read it as | Meaning |
|---|---|---|
| n × k | n times k | the kth multiple of n; for example 6 × 4 = 24 is the 4th multiple of 6 |
| 3 ∣ 12 | 3 divides 12 | 12 is a multiple of 3 (and 3 is a factor of 12) |
| LCM(4, 6) | L C M of 4 and 6 | the least common multiple of 4 and 6, which is 12 |
Key facts
- A number has infinitely many multiples but only a limited number of factors: 6 has the factors 1, 2, 3, 6 and the multiples 6, 12, 18, 24, …
- The smallest positive multiple of a number is the number itself, because n × 1 = n.
- Divisibility rules spot multiples fast: a multiple of 2 ends in 0, 2, 4, 6 or 8; a multiple of 5 ends in 0 or 5; a multiple of 3 has a digit sum that is a multiple of 3.
- If a is a multiple of b, then b is a factor of a: 18 is a multiple of 6, so 6 is a factor of 18.
- Multiples of 4 and 6 overlap at 12, 24, 36, …: these are common multiples, and 12 is the least common multiple.
Listing and testing multiples
- n
- the number whose multiples you want
- 1, 2, 3, …
- the counting numbers you multiply by; the list never ends
To test whether m is a multiple of n, divide m by n. A remainder of 0 means yes: 91 ÷ 7 = 13, so 91 is a multiple of 7. A remainder that is not 0 means no.
Multiple examples, step by step
Example 1: List the multiples
List the first five multiples of 7.
- Multiply 7 by the counting numbers 1 to 5.
- 7 × 1 = 7, 7 × 2 = 14, 7 × 3 = 21.
- 7 × 4 = 28, 7 × 5 = 35.
Answer: The first five multiples of 7 are 7, 14, 21, 28 and 35.
Example 2: Test with division
Is 96 a multiple of 6? Is 96 a multiple of 9?
- Divide by 6: 96 ÷ 6 = 16 with remainder 0.
- So 96 = 6 × 16, and 96 is a multiple of 6.
- Divide by 9: 96 ÷ 9 = 10 with remainder 6.
- The remainder is not 0, so 96 is not a multiple of 9. (Check: 9 + 6 = 15 is not a multiple of 9.)
Answer: 96 is a multiple of 6 (6 × 16) but not a multiple of 9.
Example 3: Common multiples in a schedule
Bus A leaves the station every 12 minutes and bus B every 18 minutes. Both leave at 8:00 a.m. When do they next leave at the same time?
- Bus A leaves at multiples of 12 minutes after 8:00: 12, 24, 36, 48, …
- Bus B leaves at multiples of 18 minutes: 18, 36, 54, …
- The first number on both lists is 36, the least common multiple of 12 and 18.
- 36 minutes after 8:00 a.m. is 8:36 a.m.
Answer: The buses next leave together at 8:36 a.m., 36 minutes later.
Common mistakes
A multiple is usually larger than or equal to the number, while a factor divides the number.
8 × 1 = 8, so every number is a multiple of itself, and it is the first one on the list.
You can always multiply by the next counting number, so a list of multiples never ends.
Only the rules for 2, 5 and 10 look at the last digit. The rule for 3 uses the sum of the digits.
Not to be confused with
A factor divides a number exactly; a multiple is the number times a whole number. 4 is a factor of 12, and 12 is a multiple of 4.
A multiple belongs to one number; the least common multiple is the smallest positive multiple shared by two or more numbers. For 4 and 6 it is 12.
A product is the answer to any multiplication, such as 2.5 × 4 = 10. Multiple is used for whole numbers: 10 is a multiple of 5 and of 2.
Quick check: 3 questions
Which number is a multiple of 8?
Answer: C. 56 = 8 × 7, so 56 is a multiple of 8. 4 is a factor of 8, not a multiple; 28 is a multiple of 4 but 28 ÷ 8 leaves 4; and 18 only ends in 8.Show answer and explanation
Which number is a multiple of both 3 and 4?
Answer: D. 24 = 3 × 8 = 4 × 6, so it is a common multiple. 16 is a multiple of 4 only, 18 is a multiple of 3 only, and 7 is just 3 + 4.Show answer and explanation
What is the 9th multiple of 6?
Answer: B. The 9th multiple is 6 × 9 = 54. 15 adds 6 and 9 instead of multiplying, 60 is the 10th multiple, and 48 is the 8th.Show answer and explanation
Multiple: frequently asked questions
Is 0 a multiple of every number?
Yes. Any whole number times 0 is 0, so 0 is a multiple of 1, 2, 3 and every other whole number. In school, though, lists of multiples usually start at the number itself (6, 12, 18, …), because they use the counting numbers 1, 2, 3, … When a question asks for the least common multiple, it means the smallest positive one, so 0 never counts there.
What is the difference between a multiple and a factor?
They describe the same multiplication from opposite sides. In 4 × 5 = 20, 4 and 5 are factors of 20, and 20 is a multiple of 4 and of 5. Factors are never bigger than the number (for positive numbers), and there are only a few of them. Multiples are never smaller than the number, and there are infinitely many.
How many multiples does a number have?
Infinitely many. You can always multiply by the next counting number, so the list 3, 6, 9, 12, … never ends. That is why you write three dots after the first few multiples. Factors are different: 12 has exactly six factors, 1, 2, 3, 4, 6 and 12.
Practice and tools
Sources
- Common Core State Standards, Grade 4 Operations and Algebraic Thinking (4.OA.B.4)
- OpenStax, Prealgebra 2e, 2.4 Find Multiples and Factors
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.OA.B.4
Cite this entry
Effortless Math Team. “Multiple.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/multiple/
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