Contents

# Multiple|Definition & Meaning

## Definition

**Multiple** is the result of **multiplying **a number with another number. In other words, a larger number is a multiple of a smaller number if dividing the larger number by the smaller one produces a **zero remainder**. Therefore, **6** is a **multiple** of** 2** and **3** because 2 x 3 = 6.

In mathematics, the term “**multiple of the numbers**” refers to the result of **multiplying** two whole numbers together. For example, **5** multiplied by **6** equals **30**, therefore, **30** is now a multiple of both** 5** and **6**. In accordance with this, a multiple would be a number that, when divided by the provided number, results in **no** **remainder** at the end of the division. This is the definition of a multiple for any given number.

The figure above shows the multiple of **5** and **6,** which is** 30**. These both factors are different, but when the number is multiplied by **1,** the multiple will be the number **itself**.

## Illustration of Multiples

Mathematics is the study of **numbers**, their classifications, and the ideas that are associated with them. It is a numerical game. The area of mathematics known as **arithmetic** focuses on the qualities and operations that can be performed on numerical values.

In the primary mathematics grades, the concepts of multiples and factors are studied hand in hand as two essential building blocks. A number is considered to be a **factor** if, after being used to divide another number, it does **not** produce a **remainder**.

A **multiple**, on the other hand, is a number that is arrived at by theÂ **multiplication** of a given number by another. While a number’s factors can be counted, a number’s multiples can never be exhausted. Every single number is really a multiple of both** 0** and the **number itself**.

The first multiple of the number** 7** is **7** itself because when it is multiplied with any other factor that is **1,** it results in the **same** number.

## A Deeper Dive Into Finding Multiples

The two terms, factors and multiples, may, at first glance, appear to be interchangeable; however, there are a number of key distinctions between the two that have been outlined in this article.

You can take any number with a single digit that is** not zero**, such as the number **2**, and add it to itself whatever amount of times you wish. Let’s move on and perform the addition of the number **2** five times. This can be written down as two plus two plus two plus two plus two** (2 + 2 + 2 + 2 + 2)**, and the result of the issue would be ten.

This new number will be referred to as the result of **2** times **5** from now on. Similarly, if we were to take the number **5** and add it **twice**, we would arrive at the number 10. The number 10 is the result of multiplying **5** by **2**.

The** 10** is therefore the multiple of **5** and a multiple of** 2**, as** 2** multiplied by** 5** yields **10**, while it is also a multiple of 2 as** 5** multiplied by **2** yields **10**.

If you have been following along thus far, then understanding **multiples** and all of the concepts associated with them, which are covered in this article, will be quite simple for you to do. You will have plenty of opportunities to practice along with the examples and questions provided, as was previously said.

At the conclusion of the article, you will find the answers to each of the practice questions.

## Methods To Find Multiples

There are different ways to find multiples of different numbers. Different methods to find multiples are listed below:

- Least Common Multiple
- Grid Multiplication Method

### Least Common Multiple

Discovering the number that is the** LCM** of two and more than numbers is not only a fascinating approach to solving problems, but it is also occasionally important. Finding the **least common multiples** of two or more numbers can be done through a few **different** methods.

The following are the most typical approaches: **Listing Method, Ladder Method, **and** Lcm of Mixed Numbers LCM**, etc.

The above figure shows the least common multiple of **12** and **18**.

### Grid Multiplication Method

This grid method which is also termed both the **box method** and also t**he grammar school approach** or is an effective place to begin learning multiples as well as the calculations with higher numbers that are greater than 10. Using this approach, the process of** manually multiplying** numbers is broken down into **three** distinct parts.

TheÂ **first** thing to do is toÂ construct a grid or table, with the numbers you need to multiply appearing in the first row and the first column, respectively. The first box won’t have anything put in it. The **second** stage in this process involves multiplying all of the integers that are located in the columns and the rows together. A comprehension of addition is required for the **third** level.

Utilizing this approach makes it effortless to dissect and reduce the complexity of the components that contribute to that number.

## Example Problems of Multiples

### Example 1

Write the first **8** multiples of **11** by **multiplication** and **addition** method?

### Solution

By Multiplication Method:

**11 x 1 = 11**

**11 x 2 = 22**

**11 x 3 = 33**

**11 x 4 = 44**

**11 x 5 = 55**

**11 x 6 = 66**

**11 x 7 = 77**

**11 x 8 =88**

By Addition Method:

**11**

**11 + 11 = 22**

**11 + 11 + 11 = 33**

**11 + 11 + 11 + 11 = 44**

**11 + 11 + 11 + 11 + 11= 55**

**11 + 11 + 11 + 11 + 11 + 11= 66**

**11 + 11 + 11 + 11 + 11 + 11 + 11= 77**

**11 + 11 + 11 + 11 + 11 + 11 + 11 + 11= 88**

So here, 11, 22, 33, 44, 55, 66, 77, and 88 are the multiples of 11.

### Example 2

Write some common multiples of **5** and **10**.

### Solution

Multiple of 5:

**5, 10, 15, 20, 25, 30, 35, 40, 45, 50**

Multiples of 10:

**10, 20, 30, 40, 50**

So the common multiples of 5 and 10 are **10, 20, 30, 40,** and** 50.**

*All the figures above are created on GeoGebra.*