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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

What is a multiple? (Definition)

A multiple of a number $n$ is another number calculated by multiplying $n$ by an integer (relative).

Example: $k \times x$ is a multiple de $x$ (with $k \in \mathbb{Z}$)

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 integer numbers?

dCode has a tool to calculate the LCM (least common multiple) of two numbers. Other 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 (and -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.

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