**Multiples **

A multiple is referred to as a product of an integer or any quantity. In simple terms, a multiple is a number divided by another number for a certain time without remaining. A multiple can also be described as a number that you get when you multiply one whole number by another whole number. Multiplication tables are used to find multiples.

Let’s look at the simple illustration. For instance, here are the first five (non-zero) multiples of 6. They are 6, 12, 18, 24, and 30. Another example is 4×5=20. Therefore, 20 is a multiple of 4 and 5. Furthermore, the multiples of 4 are 4(4×1=4), 8(4×2=8), 12(4×3=12), etc. Moreover, multiples help you to explore and understand mathematical concepts.

Let’s get started to learn more about multiples.

**Types of Multiples**

**Multiples** –** **The numbers you get by multiplying a number by natural numbers. E.g. 1, 2, 3, 4, 5, 6,…

**Common Multiples** – It refers to a whole number that is a shared multiple by at least two numbers.

**Least Common Multiple (LCM**) – Refers to the smallest common multiple shared by two or more integers

**Solved examples **

Example 1: Find the multiples of 517

Multiply 517 by any natural numbers (Note multiples are infinite hence we will list a few)

517 × 1= **517**

517 × 2 = **1034**

517 × 3 = **1551**

517 × 4 = **2068**

517 × 5 = **2585**

517 × 6 = **3102**

517 × 7 = **3619**

517 × 8= **4136**

517 × 9= **4653**

517 × 10= **5170**

** **The multiples of 517** are 517, 1034, 1551, 2068, 2585, 3102, 3619, 4136, 4653, 5170 …….**

**Example 2: Find the multiples of 90 **

Multiply 90 by random natural positive numbers

90 × 1= **90**

90 × 2= **180**

90 × 3 = **270**

90 × 4 = **360**

90 × 5 = **450**

90 × 6 = **540**

90 × 7 = **630**

90 × 8 = **720**

90 × 9 = **810**

90 × 10 = **900**

The multiples of 90 are: **90, 180, 270, 360, 450, 540, 630, 720, 810, 900…..**

**Multiples tutorial video**

**Interesting properties about Multiples**

● The least multiple of a given number is the number itself. It is because every number can be multiplied by 1 and get the same number.

● Each multiple of a number is either greater than or equal to the number. For instance, multiples of 3 are 3, 6, 9, 12, 15, 28, etc.

● All multiples of number 2 are even numbers. They include 2,4,6,8,20,12,14 etc.

● The number of multiples of a number is infinite. For instance, multiples of 5 are 5, 10, 15, 20, 25, 30 etc.

● The smallest common multiple for at least two numbers is known as the Least Common Multiple LCM

● Each number is a multiple of itself

● Every number is a multiple of 1

● Zero is a multiple of every number because every number multiplied by zero is zero

**List of multiples **

Here is a list of the first 12 multiples of 12 the first 12 numbers;

● Multiples of 1 are 1,2,3,4,5,6,7,8,9,10,11, and 12.

● Multiples of 2 are 2,4,6,8,10,12,14, 16,18,20,22, and 24.

● Multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33 and 36.

● Multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44 and 48.

● Multiples of 5 are 5,10, 15,20,25,30,35,40,45,50,55 and 60.

● Multiples of 6 are 6,12,18,24,30,36,42,48,54,60,66 and 72.

● Multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77, and 84.

● Multiples of 8 are 8,16,24,32,40,48,56,64,72,80,88, and 96.

● Multiples of 9 are 9,18,27,36,45,54,63,72,81,90,99, and 108.

● Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,110 and 120.

● Multiples of 11 are 11,22,33,44,55,66,77,88,99,110,121 and 132.

● Multiples of 12 are 12, 24,36,48,60,72,84,96,108,120,132,and 144.

**Other solved examples**

What are the multiples of 201?

What are the multiples of 547?

What are the multiples of 633?

What are the multiples of 1001?

What are the multiples of 2039?