GCSE Maths Number

FMP

Factors And Multiples

Multiples

# Multiples

Here we will learn about multiples, including how to calculate multiples of a number, identify common multiples, and solve problems using knowledge of multiples.

There are also multiples worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

## What are multiples?

Multiples are the result of multiplying a number by an integer.

For example, the first 5 multiples of 7 are: 7, 14, 21, 28, and 35.

Multiples can be integers, decimals, fractions, negative numbers or surds, and can sometimes be called products.

The product of two or more factors is a multiple, and every integer is a multiple of two or more factors.

In general, if n is any number and x is an integer, m is a multiple of n where

n\times{x}=m .

To calculate a multiple of a number n , you have to multiply it by an integer. You can list multiples of a number by multiplying n by the position of the value in the list.

For example, the 9th multiple of 4 is equal to 9 \times 4=36.

### What are multiples? ## How to calculate multiples

In order to calculate multiples of a number n:

1. State the first multiple of \textbf{n} .
2. Calculate the second multiple of \textbf{n} .
3. Continue until you have calculated the number of multiples needed.
4. Write the solution.

### Explain how to calculate multiples ## Multiples examples

### Example 1: listing multiples (single digit number)

List the first 5 multiples of 8.

1. State the first multiple of \textbf{n} .

The first multiple of 8 is

8\times{1}=8.

2Calculate the second multiple of \textbf{n} .

The second multiple of 8 is

8\times{2}=16.

3Continue until you have calculated the number of multiples needed.

\begin{aligned} &8\times{3}=24. \\\\ &8\times{4}=32. \\\\ &8\times{5}=40. \end{aligned}

4Write the solution.

The first 5 multiples of 8 are 8, 16, 24, 32, and 40.

### Example 2: listing multiples (decimal)

List the first 5 multiples of 1.2.

The first multiple of 1.2 is

1.2\times{1}=1.2.

The second multiple of 1.2 is

1.2\times{2}=2.4.

\begin{aligned} &1.2\times{3}=3.6. \\\\ &1.2\times{4}=4.8. \\\\ &1.2\times{5}=6. \end{aligned}

The first 5 multiples of 1.2 are 1.2, 2.4, 3.6, 4.8, and 6.

### Example 3: listing multiples (negative number)

List the first 5 multiples of -4.

The first multiple of -4 is

-4\times{1}=-4.

The second multiple of -4 is

-4\times{2}=-8.

\begin{aligned} &-4\times{3}=-12. \\\\ &-4\times{4}=-16. \\\\ &-4\times{5}=-20. \end{aligned}

The first 5 multiples of -4 are -4, -8, -12, -16, and -20.

### Example 4: calculate a specific multiple

What is the 9th multiple of 7?

You only need to calculate the 9th multiple of 7 so you can move on to step 2.

It is worth noting here that you are looking at the multiples of 7.

Move on to step 3.

The 9th multiple of 7 is equal to

7\times{9}=63.

The 9th multiple of 7 is 63.

### Example 5: calculate a specific multiple

What is the 4th multiple of -1.8?

As you only need to calculate the 4th multiple of -1.8, you can move on to step 2.

It is worth noting here that you are looking at the multiples of -1.8.

Move on to step 3.

The 4th multiple of -1.8 is equal to

-1.8\times{4}=-7.2.

The 4th multiple of -1.8 is -7.2.

### Example 6: common multiples

Given that the first 5 multiples of 8 are 8, 16, 24, 32, and 40, find a common multiple of 6 and 8.

The first multiple of 6 is

6\times{1}=6.

The second multiple of 6 is

6\times{2}=12.

\begin{aligned} &6\times{3}=18. \\\\ &6\times{4}=24. \end{aligned}

The first common multiple of 6 and 8 is 24.

### Common misconceptions

• Factors and multiples

Factors and multiples are easily mixed up. Remember multiples are the multiplication table, whereas factors are the numbers that go into another number without a remainder.

• Remember the number itself for factors and multiples

All numbers are a multiple of themselves.

For example, the multiples of 6 are 6, 12, 18, 24 and so on and so 6 is a multiple of itself.

### Practice multiples questions

1. List the first 5 multiples of 12.

1, 2, 3, 4, 6 12, 24, 36, 48, 60 12, 17, 22, 27, 32 12\times{5}=60 \begin{aligned} &12\times{1}=12 \\\\ &12\times{2}=24 \\\\ &12\times{3}=36 \\\\ &12\times{4}=48 \\\\ &12\times{5}=60 \end{aligned}

So, the first 5 multiples of 12 are 12, 24, 36, 48, and 60.

2. List the first 5 multiples of 2.3.

2.3, 5.29, 12.167, 27.9841, 64.36343 2.3, 7.3, 12.3, 17.3, 22.3 2.3, 4.6, 6.9, 9.2, 11.5 2.3\times{5}=11.5 \begin{aligned} &2.3\times{1}=2.3 \\\\ &2.3\times{2}=4.6 \\\\ &2.3\times{3}=6.9 \\\\ &2.3\times{4}=9.2 \\\\ &2.3\times{5}=11.5 \end{aligned}

So, the first 5 multiples of 2.3 are 2.3, 4.6, 6.9, 9.2, 11.5.

3. List the first 5 multiples of -6.

-6, -12, -18, -24, -30 -6, 12, -18, 24, -30 -6, -11, -16, -21, -26 -6\times{5}=-30 \begin{aligned} &-6\times{1}=-6 \\\\ &-6\times{2}=-12 \\\\ &-6\times{3}=-18 \\\\ &-6\times{4}=-24 \\\\ &-6\times{5}=-30 \end{aligned}

So, the first 5 multiples of -6 are -6, -12, -18, -24, and -30.

4. What is the 8th multiple of 9?

9, 18, 27, 36, 45, 54, 63, 72 72 17 1.125 9\times{8}=72.

5. What is the 6th multiple of -2.5?

-2.5, 5, -7.5, 10, -12.5, 15 -12.5 -2.4 -15 -2.5\times{6}=-15.

6. The first 6 multiples of 4 are 4, 8, 12, 16, 20 and 24. By calculating the multiples of 6, determine the first 2 common multiples of 4 and 6.

6, 12, 18, 24, 30 1, 2, 3 12, 24 24, 48, 72 The first 5 multiples of 6 are 6, 12, 18, 24, and 30.

The first common factor of 4 and 6 is 12 and the second is 24.

### Multiples GCSE questions

1. Below is a list of numbers,

2, \ 4, \ 5, \ 7, \ 8, \ 12, \ 15, \ 24 .

(a) Which numbers are multiples of 4?

(b) Which numbers are multiples of 3?

(c) Which numbers are 1 more than a multiple of 7?

(d) Which number is a multiple of two other numbers in the list?

(4 marks)

(a) 4, 8, 12, 24

(1)

(b) 12, 15, 24

(1)

(c) 8, 15

(1)

(d) 8\ ( = 2 \times 4)

(1)

2. (a) The Venn diagram below shows the two sets F=\{ Multiples of 4\} and T=\{ Multiples of 10\}.

\xi=\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40\}

Place all of the numbers from this set on to the Venn diagram. (b) What is the lowest common multiple of 4 and 10?

(3 marks)

(a)

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

(1)

Multiples of 10: 10, 20, 30, 40

(1)

Completed Venn diagram

(1) (b) 20

(1)

3. An ice cream stand sells vanilla ice cream in a single cone with raspberry sauce.

Single cones are sold in packs of 50.

Ice cream tubs contain 20 portions of ice cream.

A bottle of raspberry sauce serves 40.

Kevin wants to buy the same number of servings of ice cream, cones and raspberry sauce.

What is the smallest number of tubs of ice cream he would need to buy?

(3 marks)

Multiples of 50, 20 and 40 listed.

(1)

200 of each ingredient.

(1)

200\div{20}=10 tubs of ice cream.

(1)

## Learning checklist

You have now learned how to:

• Find factors and multiples
• Write numbers as a product of their prime factors
• Find the lowest common multiple
• Find the highest common factor

## Still stuck?

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#### FREE GCSE Maths Practice Papers - 2022 Topics

Practice paper packs based on the advanced information for the Summer 2022 exam series from Edexcel, AQA and OCR.

Designed to help your GCSE students revise some of the topics that will come up in the Summer exams.