# Multiples

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 1 Concept Video on Multiples 2 Introduction to Multiples 3 Understanding Multiples 4 Tips and Tricks 5 List of a few multiples 6 Properties of Multiples 7 Solved Examples on Multiples 8 Important notes on Multiples 9 Practice Questions on Multiples 10 Maths Olympiad Sample Papers 11 Frequently Asked Questions (FAQs) 12 Download FREE Worksheets on Multiples

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## Concept Video on Multiples

Before we begin explaining Multiples, let us first get an idea of the concept with the help of this simple video.

In this video you will see how Cuemath students visualise Multiples using Fraction rods.

## Introduction to Multiples

### Definition of Multiples

Multiples are numbers that we get when we multiply one whole number by another whole number.

Or in simple terms, you get the multiples of a number when you multiply!

Do you remember the multiplication tables?

We will be using them to find multiples.

Let us see how it helps us while we list the first five multiples of the number 6

The first five multiples of 6 are:

6, 12, 18, 24, 30

The 1st multiple of 6 : ($$6 \times 1 = 6$$)

The 2nd multiple of 6 : ($$6 \times 2 = 12$$)

The 3rd multiple of 6 : ($$6 \times 3 = 18$$)

The 4th multiple of 6 : ($$6 \times 4 = 24$$)

The 5th multiple of 6 : ($$6 \times 5 = 30$$)

You can see that the multiples of 6 are in the table of 6

Here are some additional multiples of 6:

 Multiple of a number = The number $$\times$$ Any integer (not a fraction)

Let us place numbers in the above equation.

$$12 = 6 \times 2$$

We see that 12 is a multiple of 6

### Observe:

In the example,

$$6 \times 2 = 12$$

12 is a multiple of 6 and a multiple of 2 as well.

## Understanding Multiples

Multiples are studied as an important concept in Maths.

Let us look at an example.

Example:

Have you ever stacked up and played with building blocks?

When you place or stack these building blocks on top of each other, you end up making towers.

They may look like this:

If you look carefully at the numbers printed on the blocks and add them, the result is a bigger number which is made up of those numbers.

These bigger numbers are known as the multiples of that number.

Here, the multiples of 2 are 2, 4, 6, 8, 10, 12 and so on.

Towers Made up of Gives these multiples
Tower 1 1 block of 2 2
Tower 2 2 blocks of 2 4
Tower 3 3 blocks of 2 6
Tower 4 4 blocks of 2 8
Tower 5 5 blocks of 2 10
Tower 6 6 blocks of 2 12

It continues this way and there could be infinite towers giving infinite multiples.

### A Jumping Game of Multiples

Let us play a simple game.

There is a track marked with numbers.

You have to jump on every third tile without stepping on any number in between.

Amit starts jumping from number 3

Let us colour each 3rd tile as he jumps on the track.

If you list the tiles that he jumps on, you can observe that they are multiples of 3

3, 6, 9, 12, 15, 18,......

Tips and Tricks

Here are few ways to find multiples:

 1. Add the number to itself repeatedly: 4 + 4 = 8, 8 + 4 = 12, 12 + 4 = 16, etc. 2. Skip count: 5, 10, 15, 20, 25, etc. 3. Multiply the number with 1, 2, 3, 4 and so on: $$2 \times 1 = 2$$, $$2 \times 2 = 4$$, $$2 \times 3 = 6$$, $$2 \times 4 = 8$$, etc.

## List of a few Multiples

First ten multiples of Multiples
3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
10 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

## Properties of Multiples

 Every number is a multiple of itself

For example, the first multiple of 7 is 7 because:

$$7 \times 1 = 7$$

 The multiples of a number are infinite

We know that numbers are infinite.

Therefore, the multiples of a number are infinite.

For example, if we need to list the multiples of 3, we start with:

3, 6, 9, 12, 15, 18…..

However, will you be able to list all the multiples here?

No, because they are infinite.

 The multiple of a number is greater than or equal to the number itself.

For example, if we take the multiples of 5

5, 10, 15, 20, 25, 30…

We can see that:

The 1st multiple of 5 is equal to 5

( $$5 \times 1 = 5$$ )

The 2nd multiple, the 3rd multiple and the following multiples of 5 are all greater than 5 (10 > 5, 15 > 5,...)

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## Solved Examples on Multiples

 Example 1

There are some fresh and delicious oranges in the orchard.

Can you number the orange trees in order and spot the trees which have fruits?

Which series of multiples is being followed here?

Solution:

We will begin numbering the trees as

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

You can notice that the series of the trees which have oranges are 3, 6, 9, and 12

This shows that they are multiples of 3

 $$\therefore$$ Multiples of 3 are followed
 Example 2

Four friends Ria, Joe, Sam and Tom decided to pluck flowers from the garden in the order of the first four multiples of 7

Can you list the number of flowers that each of them plucked as a series of the first four multiples of 7?

Solution:

The first 4 multiples of 7 are 7, 14, 21 and 28 because:

\begin{align} 7 \times 1 &= 7 \\ 7\times 2 &=14 \\ 7\times 3 &=21\\ 7 \times 4 &=28 \end{align}

Thus, Ria plucked 7 flowers.

Joe plucked 14 flowers.

Sam plucked 21 flowers.

Tom plucked 28 flowers.

 $$\therefore$$ Plucked flowers are 7, 14, 21 and 28

 Example 3

Tina attends music classes every fifth day.

Starting from the 5th of August, can you colour those dates in the calendar?

Write down the series to check the number whose multiples are shown.

Solution:

After colouring every 5th day, the series that we get is:

5, 10, 15, 20, 25, 30, ...

 $$\therefore$$ Multiples of 5 are shown
 Example 4

Ann loves watering plants.

Her teacher asked her to water the pots which were marked in the order of the multiples of 9

However, she missed a few pots.

Can you help her identify the pots that she missed?

Solution:

9, 18, __, 36, __, 54, 63, 72, __

Let us start counting the tables of 9

\begin{align} 9 \times 1 &= 9 \\ 9\times 2 &=18 \\ 9\times 3 &=27\\ 9 \times 4 &=36 \\ 9\times 5 &=45 \\ 9\times 6 &=54 \\ 9\times 7 &=63\\ 9\times 8 &=72\\ 9\times 9 &=81 \end{align}

 $$\therefore$$ The missed pots are 27, 45 and 81

Important Notes
1. Multiples are what you get after multiplying a number by an integer.
2. The symbol used to find the multiples of a number is the common multiplication symbol.
3. The 1st and smallest multiple of any number is the number itself ($$3 \times 1 = 3$$)
4. Every multiple of a number is greater than or equal to the number itself.
5. Multiples of a number are infinite. There is no largest multiple of a number.
6. Every number is a multiple of 1 ($$6 \times 1 = 6$$)

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## Practice Questions

Try these Practice Questions in the Multiples Sheet given below.

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. What is a multiple in Maths?

Multiples are numbers that result when we multiply one whole number by another whole number.

For example, in $$3 \times 4 = 12$$, 12 is the multiple of 3 and 4

## 2. What are the first four multiples of 25?

The first four multiples of 25 are 25, 50, 75 and 100

## 3. What are multiples and factors?

The multiple of a number is calculated by multiplying it with another number.

Whereas factors are the numbers that are multiplied to get a product.

## 4. What is a multiple of 4?

The multiples of 4 are 4, 8, 12, 16, and so on.

## 5. What is a multiple of 2?

2 can have many multiples like 2, 4, 6, 8, 10, and so on.

Divisibility
Divisibility
Factors and Multiples
Factors and Multiples
Divisibility
Divisibility