Multiples
A multiple is a product that we get when one number is multiplied by another number. For example, if we say 4 × 5 = 20, here 20 is a multiple of 4 and 5. The other multiples of 4 can be listed as 4 (4 ×1 = 4), 8 (4 × 2 = 8), 12 (4 × 3 = 12), and so on. Learning about multiples helps us to explore many other concepts in math, so let's get started!
1.  What are Multiples? 
2.  List of Multiples 
3.  Properties of Multiples 
4.  Factors and Multiples 
5.  Common Multiples 
6.  FAQs 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 (non zero) multiples of the number 6. The first five (non zero) multiples of 6 are 6, 12, 18, 24, and 30. We can see that the multiples of 6 are listed in the table of 6.
Hence, we can conclude that: Multiple of a number = Number × Any integer (not a fraction).
List of Multiples
We can list the multiples of a number by multiplying the given number to an integer (negative or positive). Notably, a number may have an infinite number of multiples. Here is a list of the multiples of a few numbers.
Number  First Ten Multiples (Non Zero) 

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
The properties of multiples tell us about them in detail. Here are some of the properties of multiples that tell us about the nature of multiples.
1) Every number is a multiple of itself.
For example, the first nonzero multiple of 7 is 7 because 7 × 1 = 7.
2) 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, …. and so on. However, will you be able to list all the multiples here? No, because they are infinite.
3) The multiple of a number is greater than or equal to the number itself (except for 0).
For example, let us take the multiples of 5: 5, 10, 15, 20, 25, 30, .… and so on. We can see that: The 1st multiple of 5 is equal to 5 × 1 = 5. The 2nd multiple, the 3rd multiple, and the following multiples of 5 are all greater than 5 (10 > 5, 15 > 5, ....).
Factors and Multiples
Factors and multiples are related to each other. A factor is a number that divides another number completely without any remainder, while a multiple is a product that is obtained when one number is multiplied by another number. For example, in 3 × 4 = 12, 3 and 4 are the factors of 12, while 12 is a multiple of 3 and 4.
Common Multiples
A common multiple is a number that is a shared multiple for a given set of numbers. In other words, the multiples that are common to two or more numbers are termed as the common multiples of those numbers. For example, the multiples of 3 can be listed as 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on. The multiples of 4 can be listed as 4, 8, 12, 16, 20, 24, 28, 32, 36, and so on. Now, if we identify the common multiples of 3 and 4 in these two lists, we get 12 and 24.
Multiples of Numbers:
 Multiples of 8
 Multiples of 9
 Multiples of 10
 Multiples of 11
 Multiples of 12
 Multiples of 13
 Multiples of 14
 Multiples of 15
 Multiples of 16
 Multiples of 17
 Multiples of 18
 Multiples of 20
 Multiples of 21
 Multiples of 24
 Multiples of 25
 Multiples of 30
 Multiples of 45
 Multiples of 60
 Multiples of 100
Multiples Examples

Example 1: 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 (excluding zero)?
Solution:
The first four multiples of 7 are (7 × 1) = 7, (7 × 2) = 14, (7 × 3) = 21, and (7 × 4) = 28. Hence, Ria plucked 7 flowers, Joe plucked 14 flowers, Sam plucked 21 flowers and Tom plucked 28 flowers.

Example 2: 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 in the following list: 9, 18, __, 36, __, 54, 63, 72, __?
Solution:
Let us start counting the multiplication table of 9: 9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27, 9 × 4 = 36, 9 × 5 = 45, 9 × 6 = 54, 9 × 7 = 63, 9 × 8 = 72, 9 × 9 = 81.
∴ The missed pots are 27, 45, and 81.

Example 3: List down the first five multiples of 12.
Solution:
The first five multiples of 12 can be found by multiplying 12 by the first five natural numbers.
12 × 1 = 12
12 × 2 = 24
12 × 3 = 36
12 × 4 = 48
12 × 5 = 60
∴ The first five multiples of 12 are 12, 24, 36, 48, and 60..
FAQs on Multiples
What is a Multiple in Math?
Multiples, in math, are numbers that we get when we multiply one whole number by another whole number. For example, in 7 × 5 = 35, 35 is the multiple of 7 and 5.
How are Factors and Multiples Related?
A factor is a number that divides another number completely without any remainder. A multiple is a product that is obtained when one number is multiplied by another number. For example, in 6 × 8 = 48, 6 and 8 are the factors of 48, while 48 is a multiple of 6 and 8.
What are Common Multiples?
Common multiples of any two numbers are the multiples that are common to both the given numbers. For example, the multiples of 3 can be listed as 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Similarly, the multiples of 5 can be listed as 5, 10, 15, 20, 25, 30. Now, if we identify the common multiples of 3 and 5 in these two lists, we get 15 and 30. Note that there are infinite common multiples of any set of numbers. Common multiples of two numbers can be found by finding the multiples of the LCM of those two numbers.
How to Find Multiples of a Number?
We get the multiples of a number when we multiply the given number by another number. In other words, a multiple is a product that we get when one number is multiplied by another number. For example, if we say 8 × 5 = 40, here 40 is a multiple of 8 and 5. The other multiples of 8 can be listed as 8 (8 ×1 = 8), 16 (8 × 2 = 16), 24 (8 × 3 = 24), and so on.
How many Multiples does a Number Have?
There is no limit to the multiples of a number. In other words, a number has an uncountable or infinite number of multiples.
What are the Multiples of 5?
The multiples of 5 can be found by the following method: 5 (5 × 1 = 5), 10 (5 × 2 = 10), 15 (5 × 3 = 15), and so on. Hence, they can be listed as: 5, 10, 15, 20, 25, and so on.
What are the Multiples of 4?
The multiples of 4 are 4, 8, 12, 16, 20, and so on. These can be calculated by the simple way of multiplication. 4 (4 ×1 = 4), 8 (4 × 2 = 8), 12 (4 × 3 = 12), and so on.
What are the Multiples of 2?
The multiples of 2 can be listed as 2, 4, 6, 8, 10, 12, and so on. Interestingly, this is also a list of all even numbers since all even numbers are multiples of 2.
How do you Explain Multiples?
Multiples are products that we get when we multiply one whole number by another whole number. For example, 2 × 3 = 6. Here 6 is the multiple of 3 and 2. The other multiples of 2 can be listed as 2, 4, 6, 8, 10, 12, and so on.
What are the Multiples of 3?
The multiples of 3 can be listed as 3, 6, 9, 12, 15, and so on. These multiples can be calculated by simply multiplying 3 with the counting numbers, like, 3 (3 ×1 = 3), 6 (3 × 2 = 6), 9 (3 × 3 = 9), and so on.
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