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Multiples of a Number

Tool to list multiples of a number. A multiple of a number is another number calculated with the product of this number by an integer.

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Multiples of a Number -

Tag(s) : Arithmetics, Series

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# Multiples of a Number

## Calculus of common multiples to 2 numbers

### Lowest/Smallest common multiple LCM

Tool to list multiples of a number. A multiple of a number is another number calculated with the product of this number by an integer.

### How to list multiples of a number?

Take a number and multiply it by a quantity/factor/coefficient (2, 3, 4 etc.) to get a multiple.

It exists an infinite number of multiples, so it is impossible to list all multiples of a given number, dCode suggest to fix an upper and lower bound (all multiples between A and B).

Example: $N = 3$, so $N \times 2 = 6$, $6$ is a multiple of $3$,
$N \times 3 = 9$, $9$ is a multiple of $3$, etc.

 Multiples of 1 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... Multiples of 2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... Multiples of 3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... Multiples of 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... Multiples of 5 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ... Multiples of 6 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... Multiples of 7 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ... Multiples of 8 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ... Multiples of 9 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ... Multiples of 10 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ... Multiples of 11 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, ... Multiples of 12 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ... Multiples of 13 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ... Multiples of 14 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... Multiples of 15 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

For school multiplications, use a calculator here (link)

### How to find if a number A is a multiple of B?

Divide A by B, if the rest of the Euclidean division is 0, then A is a multiple of B, and B is a divisor of A.

Example: Is 60 a multiple of 4? Divide 60 by 4, 60/4 = 15 (integer without decimals after the decimal point), remain 0, so 60 is a multiple of 4 and 4 is a divisor of 60.

Example: Is 22 a multiple of 4? Divide 22 by 4, 22/4 = 5.5 (non-integer number, with decimals after decimal point) ie 22/4 = 5 + remainder 2, so 22 is not a multiple of 4 and 4 is not a divisor of 22.

### How to find common multiples between two integers numbers?

dCode has a tool to calculate the LCM (least common multiple) of two numbers. Others multiples are multiples of the given LCM.

Example: The LCM for $3$ and $8$ is $24$, the multiples common to $3$ and $8$ are all the multiples of $24$ : $24, 48, 72, 96, ...$

### Is zero 0 a multiple?

Yes, in theory, 0 is multiple of all numbers because whatever $n$, $0 / n = 0$. In practice, it is often omitted from the list of multiples.

Zero is a multiple of every integer (except itself)

### Are all numbers multiple of 1?

Yes, all numbers are multiples of 1, but it is wrong to say that 1 is a multiple of all numbers, but it is true to say that 1 is a divisor of all numbers.

## Source code

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