CalConverters

Multiples Calculator

List the multiples of any positive integer, up to 1,000 at a time, optionally starting above a chosen minimum, with the formula shown step by step.

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How to use this calculator

Enter a positive whole number, how many multiples you want (up to 1,000), and — optionally — a minimum value the multiples must exceed. The calculator lists them in order and shows the arithmetic behind the starting point.

Tip: Multiples are the building block behind the least common multiple (LCM): the LCM of several numbers is the smallest value that shows up in every one of their multiple lists.

What is a multiple?

A multiple of a whole number nn is the result of multiplying nn by a positive integer kk:

n×k,k=1,2,3,…n \times k, \quad k = 1, 2, 3, \dots

The multiples of 5 are 5, 10, 15, 20, 25, … — an endless list, since there is no largest integer kk.

Multiples vs. factors

These two ideas are opposites and easy to mix up:

Factors of 12Multiples of 12
Definitiondivide into 1212 times an integer
Values1, 2, 3, 4, 6, 1212, 24, 36, 48, …
Sizenever larger than 12never smaller than 12
How manyfiniteinfinite

Starting above a minimum

Without a minimum, the list simply starts at k=1k = 1 (the number itself). With a minimum mm, the calculator finds the first multiple strictly greater than mm using floor division:

n×(⌊mn⌋+k),k=1,2,3,…n \times \left( \left\lfloor \frac{m}{n} \right\rfloor + k \right), \quad k = 1, 2, 3, \dots

This works even when mm is itself an exact multiple of nn: the +1+1 guarantees the result is strictly greater than mm, never equal to it.

Worked example — 100 multiples of 5, greater than 100

⌊100/5⌋=20\lfloor 100 / 5 \rfloor = 20, so the first multiple greater than 100 uses k=20+1=21k = 20 + 1 = 21:

5×21=1055 \times 21 = 105

Counting up by 5 from there gives 105, 110, 115, 120, …, all the way to the 100th value, 5×120=6005 \times 120 = 600.

Multiples and the LCM

Multiples are the foundation of the least common multiple (LCM): the LCM of two or more numbers is the smallest number that appears in every one of their multiple lists. Listing multiples side by side and spotting the first shared value is one hands-on way to find it.

Limits

To keep results exact and instant, the number is capped at 101210^{12}, the optional minimum at 101510^{15}, and the list at 1,000 multiples per request.

Frequently asked questions

What is a multiple of a number?
A multiple of nn is the product of nn and a positive integer: n×1,n×2,n×3,…n \times 1, n \times 2, n \times 3, \dots. The multiples of 3 are 3, 6, 9, 12, 15, and so on, forever.
What are the first 5 multiples of 7?
7, 14, 21, 28, and 35 — each is 7 times the next counting number (7×1,7×2,…,7×57 \times 1, 7 \times 2, \dots, 7 \times 5).
How do I find multiples greater than a certain number?
Divide the minimum by nn and round down (floor), then add 1 to get the first qualifying multiplier kk. For multiples of 5 greater than 100: ⌊100/5⌋+1=21\lfloor 100 / 5 \rfloor + 1 = 21, so the first multiple is 5×21=1055 \times 21 = 105.
What is the difference between a multiple and a factor?
A factor divides evenly *into* a number; a multiple is that number multiplied *out*. 3 is a factor of 12 (since 12÷3=412 \div 3 = 4), while 12 is a multiple of 3 (since 3×4=123 \times 4 = 12).
How are multiples related to the least common multiple (LCM)?
The LCM of two or more numbers is the smallest value that appears in every one of their multiple lists — the smallest common multiple. Listing multiples side by side is one way to find it by hand for small numbers.
Why is there a limit on the number, the minimum, and the count?
The calculator caps the number at 101210^{12} and the optional minimum at 101510^{15}, and generates at most 1,000 multiples at a time, so results stay exact and instant.

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