# Multiples

The product of a quantity and an integer is called a multiple.

## Introduction

A quantity can be multiplied by any integer. The product of them is calculated by the multiplication. So, the product of them is called as multiple of the quantity.

### Example

$5$ is a quantity and it is multiplied by an integer $3$.

$5 \times 3 \,=\, 15$

The product of them is $15$ and it is formed by the multiplication. Therefore, the number $15$ is called a multiple of $5$.

Similarly, multiply the quantity $3$ by an integer $5$.

$3 \times 5 \,=\, 15$

The product of them is $15$ and it is also called as the multiple of $3$.

Therefore, the number $15$ is called as the multiple of $5$ and also multiple of $3$ in this case because the quantities $5$ and $3$ are integers mathematically.

#### Representation

A multiple is simply denoted by $M$ and the multiples of a quantity is represented by $M$ subscript the quantity. For example, the multiples of $6$ is written as $M_6$ in mathematics.

#### Examples

Let us find the multiples of $6$. For obtaining the multiplies of $6$, multiply the $6$ by the integers.

$6 \times 1 \,=\, 6$

$6 \times 2 \,=\, 12$

$6 \times 3 \,=\, 18$

$6 \times 4 \,=\, 24$

$6 \times 5 \,=\, 30$

$\vdots$

$6$, $12$, $18$, $24$, $30$ and so on are called as the multiples of $6$. It is simply written in mathematical form as follows.

$M_6 \,=\, 6, 12, 18, 24, 30, \ldots$

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