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What is a multiple in math?

In standard English multiple means manifold. But in math, a multiple is the product that we get when we multiply a number with another number. While calculating product it should be kept in mind that another number should be an integer (positive or negative).

It should not be in fraction. So, a multiple is the result of multiplication of two numbers. Let us take an example to clear the concept.

Example 1

Now, if we multiply 14 and 5 we get 70 that is

14 x 5 = 70

Here, 70 is the multiple of 14 and 5.

Example 2

16 x 1 = 6

16 x 2 = 32

16 x 3 = 48

16 x 4 = 64

16 x 5 = 80

Here 6, 32, 48, 64, 80 are the multiples of 16. We can also say that these are the first six multiples of 16.

16 is the first multiple of 16, 32 is the second multiple of 16, 48 is the third multiple of 16 and so on.

From above examples we can conclude that

nth Multiple of a number  =  number  *   n

Problems Solution
7th multiple of 8 8 * 7 = 56
3rd multiple of 12 12 * 3 = 36
6th multiple of 15 15 * 6 = 90
First five multiples of 12 12, 24, 36, 48, 60

 

Properties of Multiple

  • Every number is a multiple of itself and 1.
  • The multiples of a number are infinite.
  • The multiple of a number is greater than or equal to the number itself.
  • If a * b * c = d, then d is the known as the multiple of a, b and d.
  • Any number that is a multiple of 2 is an even number.
  • A number which is not a multiple of 2 is called an odd number.
  • Least common multiple of any number is it’s first multiple i.e. the number itself.
  • A number that is a multiple of 1 and itself only is called a prime number.

For any number:  d x 1 = d  (here, d (product) is the multiple of d and 1)

For example: 2 x 1 =2

3 x 1 = 3

5 x 1 = 5

7 x 1 = 7

So, we can see that 2, 3, 5, 7 are multiples of themselves and 1 only. These are called prime numbers.

Method to find common multiples of two or more given numbers:

The Listing Method

For two or more given numbers we find the common multiples by listing all the multiples.

For Example:

For finding common multiples of 3, 6 and 9, we first have to list down all the multiples till we start getting some common ones.

The multiple listing of 3 is: 3, 6, 9, 12, 15, 18, 21, 24. 27, 30, 33, 36…

The multiple listing of 6 is: 6, 12, 18, 24, 30, 36, 42…

The multiple listing of 9 is: 9, 18, 27, 36, 45…

So, here we can see that 18, 36 are the first two common multiples followed by 36 and so on.

18 is also known as the least common multiple or LCM of 3, 6 and 8.

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