Multiples are defined as the number obtained when multiplied by other numbers. Multiplication is used to find the multiples. The factor of two or more numbers results in multiple. Scroll down this page to solve the examples on multiples. Learn how to solve problems on multiples using different properties of multiples in the examples given below.

Multiplication of the number = Main Number Ã— n; where n is an integer

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### Worked Examples on Multiples

Make use of the properties of multiples such as Every number is multiple in itself, Every multiple of a number is either greater than or equal to the number, Every number is a multiple of 1, etc to solve the problems given below.

**Example 1.**

Write first five multiples of 10.

**Solution:**

The first five multiples of 10 are

10 Ã— 1 = 10

10 Ã— 2 = 20

10 Ã— 3 = 30

10 Ã— 4 = 40

10 Ã— 5 = 50

Therefore the first five multiples of 10 are 10, 20, 30, 40, 50.

**Example 2.**

Write the first three multiples of 14.

**Solution:**

The first three multiples of 14 are

14 Ã— 1 = 14

14 Ã— 2 = 28

14 Ã— 3 = 42

Therefore the first three multiples of 14 are 14, 28 and 42.

**Example 3.**

Write the first 5 common multiples of 3 and 6.

**Solution:**

M(3) = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 41, 44….}

M(6) = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60….}

From the above multiples we can write the first 5 common multiples of 3 and 6 as 6, 12, 18, 24, 30.

**Example 4.**

Write first five multiples of

i. 21Â Â Â Â ii. 13Â Â Â iii. 17Â Â Â Â iv. 18Â Â Â Â v. 4

**Solution:**

**i. 21**

The first five multiples of 21 are

21 Ã— 1 = 21

21 Ã— 2 = 42

21 Ã— 3 = 63

21 Ã— 4 = 84

21 Ã— 5 = 105

Therefore the first five multiples of 21 are 21, 42, 63, 84, 105.

**ii. 13**

The first five multiples of 13 are

13 Ã— 1 = 13

13 Ã— 2 = 26

13 Ã— 3 = 39

13 Ã— 4 = 52

13 Ã— 5 = 65

Therefore the first five multiples of 13 are 13, 26, 39, 52, 35.

**iii. 17**

The first five multiples of 17 are

17 Ã— 1 = 17

17 Ã— 2 = 34

17 Ã— 3 = 51

17 Ã— 4 = 68

17 Ã— 5 = 85

Therefore the first five multiples of 17 are 17, 34, 51, 68, 85.

**iv. 18**

The first five multiples of 18 are

18 Ã— 1 = 18

18 Ã— 2 = 36

18 Ã— 3 = 54

18 Ã— 4 = 72

18 Ã— 5 = 90

Therefore the first five multiples of 18 are 18, 36, 54, 72, 90.

**v. 4**

The first five multiples of 4 are

4 Ã— 1 = 4

4 Ã— 2 = 8

4 Ã— 3 = 12

4 Ã— 4 = 16

4 Ã— 5 = 20

Therefore the first five multiples of 4 are 4, 8, 12, 16, 20.

**Example 5.**

Find the common multiples of 4 and 12.

**Solution:**

A common multiple is a multiple that two or more numbers having a common number.

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

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84,…

Thus the common multiples of 4 and 12 are 12, 24, 36, 48.

**Example 6.**

Write three common multiples of 6 and 8.

**Solution:**

A common multiple is a multiple that two or more numbers having a common number.

Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48,…

Multiples of 8 are 8, 16, 24, 32, 40, 48,….

Thus the common multiples of 6 and 8 are 24, 48.

**Example 7.**

Prove that every number is multiple in itself.

**Solution:**

Let us solve some problems to prove that every number is multiple in itself.

22 Ã— 1 = 22

4656 Ã— 1 = 4656

9 Ã— 1 = 9

59 Ã— 1 = 59

By writing this product we can say that any number multiplied by 1 will be always the same number.

**Example 8.**

Write the first ten multiples of 7

**Solution:**

The first ten multiples of 7 are

7 Ã— 1 = 7

7 Ã— 2 = 14

7 Ã— 3 = 21

7 Ã— 4 = 28

7 Ã— 5 = 35

7 Ã— 6 = 42

7 Ã— 7 = 49

7 Ã— 8 = 56

7 Ã— 9 = 63

7 Ã— 10 = 70

Thus the first 10 multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

M(7) = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70}

**Example 9.**

The numbers which are multiples of 2 are called ________

**Solution:**

The multiples of 2 are 2, 4, 6, 8, 10, 12, 14,….

Thus the numbers which are multiples of 2 are called Even numbers.

**Example 10.**

Write first five multiples of 90.

**Solution:**

The first five multiples of 90 are

90 Ã— 1 = 90

90 Ã— 2 = 180

90 Ã— 3 = 270

90 Ã— 4 = 360

90 Ã— 5 = 450

Thus the first five multiples of 90 are 90, 180, 270, 360 and 450.