# Multiples

Learning about multiples is one of the most interesting concepts in math. In this chapter, you will be introduced to the definition of multiples, multiple math, the meaning of multiple, and multiples of 3, along with multiple of math examples.

Check-out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions on Multiples at the end of the page.

If this is too much information to comprehend, let's go back to basics. Let's cite the example of Tom, who attends piano class every third day and Sam, who attends the same piano class every fifth day. Can you tell us when they would attend the same class together? Well, if you multiply 3 and 5, you will have your answer.

Learning about multiples helps us to get the answer to such questions as we use them further in finding the Least Common Multiple.

So let's start!

## Lesson Plan

 1 What Are Multiples? 2 Tips and Tricks 3 Solved Examples on Multiples 4 Important Notes on Multiples 5 Interactive Questions on Multiples

## What Are 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 to understand the meaning of multiples 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.

Find and learn the first five multiples of a number through this calculator. Enter numbers between 1 and 10 and calculate!

## 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.

Ann starts jumping from number 3

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

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

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

## List of a Few Multiples

Number First Ten 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, ....)

Tips and Tricks

Here are a 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: $$2 \times 1 = 2$$, $$2 \times 2 = 4$$, $$2 \times 3 = 6$$, $$2 \times 4 = 8$$, ....

## Common Multiples

Let us take the multiples of 2 and 5

The multiples of 2 are 2, 4, 6, 8, 10, 12, 18, ....

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, ....

Now, if we compare these and observe the multiples that are common in 2 and 5, we get 10, 20, ....

A common multiple of two numbers is a number that is a multiple of each of the numbers.

Representing these multiples on the number line:

Among these, the multiples that are common to each of these numbers are 10, 20, ....

These are called the common multiples of 2 and 5

## Least Common Multiple

The Least Common Multiple (LCM) of two or more numbers is the smallest number among all common multiples of the given numbers.

In the example given above, the common multiples of 2 and 5 are 10, 20, ….

The smallest number among 10, 20, … is 10

So the Least Common Multiple of 2 and 5 is 10

This can be written as:

LCM (2, 5) = 10

## 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 being 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

John attends music classes every fifth day.

Starting from August 5, 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 being 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 multiplication table 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. The 1st and smallest multiple of any number is the number itself (3 $$\times$$ 1 = 3)
2. Every multiple of a number is greater than or equal to the number itself.
3. Multiples of a number are infinite. There is no largest multiple of a number.
4. Every number is a multiple of 1 (6 $$\times$$ 1 = 6 )

## Interactive Questions

Try these Practice Questions in the Multiples Sheet given below.

## Important Topics

Given below are the list of topics that are closely connected to multiples. These topics will also give you a glimpse of how such concepts are covered in Cuemath.

## Let's Summarize

We hope you enjoyed learning about Multiples with the simulations and practice questions. Now you will be able to easily solve problems on multiple math with multiple math examples you learned today.

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

## 1. How many multiples does a number have?

A number has uncountable or infinite number of multiples.

## 2. What are the multiples of 5?

The multiples of 5 are 5, 10, 15, 20, 25, and so on.

## 3. What are the multiples of 4?

The multiples of 4 are 4, 8, 12, 16, 20, and so on.

## 4. What are the multiples of 2?

The multiples of 2 can be listed as 2, 4, 6, 8, 10, 12, and so on.

Divisibility
Divisibility
Factors and Multiples
Factors and Multiples
Divisibility
Divisibility