Multiples

Introduction  

Have you ever wondered why the number 5 keeps appearing when you count by fives? Or why do numbers like 12 appear in both the 3 and 4 times tables? The answer is found in understanding multiples.  

In this self-learning guide, we will look into what multiples are, how to find them, their real-life applications, and their connection to important math concepts like LCM and factors. With many charts, examples, and explanations, you’ll gain a solid understanding of multiples in math.

 

Table of Contents  

• What Are Multiples?
• Multiples in Maths
• Why Learn Multiples in Maths?
• Examples of Multiples
• Multiples of a Number
• Least Common Multiple (LCM)
• Multiples Chart
• Multiples List
• Difference Between Multiples and Factors
• How to Find Multiples
• Common Multiples
• Misconceptions About Multiples
• Fun Facts About Multiples
• Solved Examples
• Conclusion
• FAQs on Multiples

 

What Are Multiples?

A multiple is the product of a number and any whole number.  

In simpler terms, when you multiply a number by 1, 2, 3, 4, and so on, the results are multiples.  

Key Points:  

Every number has infinite multiples.  

The first multiple of any number is the number itself.  

You can easily explain what multiples are by thinking of the times table.  

Example of a Multiple:  

Multiples of 6: 6, 12, 18, 24, 30  

 

Multiples in Maths

In math, multiples describe numbers that belong to a specific number's multiplication pattern.  

They are fundamental for solving problems involving LCM, HCF, and fractions.  

 

Why Learn Multiples in Maths?

• They help with understanding number patterns.  

• They are useful for simplifying fractions and solving algebra problems.  

• They are essential for finding the least common multiple (LCM) in more complex problems.  

 

Examples of Multiples

Here are some quick examples:  

Examples of multiples of 3: 3, 6, 9, 12, 15  

Examples of multiples of 7: 7, 14, 21, 28, 35  

Examples of multiples of 10: 10, 20, 30, 40, 50  

 

Multiples of a Number

To find the multiples of a number, simply multiply it by counting numbers.  

For example:  

Multiples of a number like 8 = 8 × 1, 8 × 2, 8 × 3, and so on → 8, 16, 24, 32, 40  

Quick Tip: Use a multiplication table to quickly find the multiples of a number.

 

Least Common Multiple (LCM)

The least common multiple (LCM) is the smallest multiple common to two or more numbers.  

Example:  

LCM of 4 and 6  

Multiples of 4 = 4, 8, 12, 16, ...  

Multiples of 6 = 6, 12, 18, 24, ...  

LCM = 12  

 

Why LCM Is Important:  

It is used for adding or subtracting unlike fractions.  

It is crucial for solving time and work problems.  

 

Multiples Chart

Use a multiples chart to visualise and spot patterns easily.  

Multiples Chart for 1 to 10:  

 

 

 

Multiples List

A multiples list can help you find common multiples or compare them across numbers.  

Multiple List of 12 and 15:  

12: 12, 24, 36, 48, 60, 72  

15:15, 30, 45, 60, 75, 90  

Common multiple: 60  

 

Difference Between Multiples and Factors

Multiples: Results of multiplying a number.  

Factors: Numbers that divide a number exactly.  

 

Key Point: This is the difference between multiples and factors often misunderstood in early learning.

 

How to Find Multiples

Multiply the number by 1, 2, 3, and so on.  

Example:  

Find the first 5 multiples of 9:  

9 × 1 = 9  

9 × 2 = 18  

9 × 3 = 27  

9 × 4 = 36  

9 × 5 = 45  

 

Common Multiples

Common multiples are numbers that are multiples of two or more numbers.  

Example:  

Common multiples of 3 and 5: 15, 30, 45, 60  

Use: Helpful in finding the least common multiple (LCM).  

 

Misconceptions About Multiples

• Only larger numbers have multiples.  

False. Every number has infinite multiples, even 1.  

• Multiples and factors are the same.  

No, factors divide a number; multiples are products.  

• Multiples end somewhere.  

Wrong. Multiples go on forever.  

• Zero is not a multiple.  

Incorrect. Zero is a multiple of every number.  

• Multiples cannot be smaller than the number.  

No. Zero is always smaller and is a valid multiple.  

 

Fun Facts About Multiples

• Every number is a multiple of itself.  

• All even numbers are multiples of 2.  

• A number can have common multiples with several numbers.  

• Multiples appear in calendars (like 7 for the days of the week).  

• Traffic light timers often follow multiple patterns (like 30, 60, or 90 seconds).  

 

Solved Examples

Example 1:  

Find the first 4 multiples of 11.  

Answer: 11, 22, 33, 44  

 

Example 2:  

What is the LCM of 8 and 12?  

Answer: 24  

 

Example 3:  

Is 100 a multiple of 10?  

Answer: Yes. 10 × 10 = 100  

 

Example 4:  

List 3 common multiples of 3 and 4.  

Answer: 12, 24, 36  

 

Example 5:  

What is the difference between the multiples and factors of 6?  

Answer:  

Multiples: 6, 12, 18, 24, ...  

Factors: 1, 2, 3, 6  

 

Conclusion

Understanding multiples is crucial to mastering number operations and solving more complex math problems. From identifying multiples of a number to using a multiples chart or list, you can build strong math skills. Learning the difference between multiples and factors and using concepts like the least common multiple (LCM) prepares you for fractions, ratios, and algebra.  

By practising regularly and exploring examples of multiples, anyone can grasp the concept of multiples in math.

 

Related LInk

Factors:   Master factors in math with easy tricks and examples!

LCM (Least Common Multiple):  Learn how to find LCM step-by-step with real-life examples!

 

Frequently Asked Questions on Multiples

1. What is a multiple in math?

Ans: A multiple in math is the product of a number and any whole number.

 

2. How to explain multiples?

Ans: Explain multiples as the numbers you get when you multiply a number by 1, 2, 3, and so on.

 

3. What is the definition of multiple for class 6?

Ans: A multiple is a number that can be divided exactly by another number without a remainder.

 

4. How do you identify multiples?

Ans: You identify multiples by multiplying the number with counting numbers like 1, 2, 3, etc.

 

Learn all about Multiples with Orchids The International School – Simple math made fun and easy!