1. Multiples
Do you remember Multiplication Tables? We will use them to find Multiples. The numbers that we get when we multiply one whole number by another whole number are known as Multiples. In simple words, you get the multiples of a number when you multiply!
For example, To find the multiples of 5, we multiply 5 by 1, 5 by 2, 5 by 3, and so on. The multiples are the product of this multiplication.
| Example 1: | Find the multiples of whole number 5 | |||||||
| Multiplication: | 5 x 1 | 5 x 2 | 5 x 3 | 5 x 4 | 5 x 5 | 5 x 6 | 5 x 7 | 5 x 8 |
| Multiples of 5: | 5 | 10 | 15 | 2 | 25 | 30 | 35 | 40 |
Hence, the multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, …
1.1 List of Multiples of Numbers
The below table shows the first 10 multiples of a few numbers:
| Number | First 10 Multiples |
| 2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 |
| 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 |
| 6 | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 |
| 7 | 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 |
| 8 | 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 |
| 9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 |
| 10 | 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 |
| 11 | 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 |
| 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 |
| 13 | 13, 26, 39, 52, 65, 78, 91, 104, 117, 130 |
| 14 | 14, 28, 42, 56, 70, 84, 98, 112, 126, 140 |
| 15 | 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 |
| 16 | 16, 32, 48, 64, 80, 96, 112, 128, 144, 160 |
| 17 | 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 |
| 18 | 18, 36, 54, 72, 90, 108, 126, 144, 162, 180 |
| 19 | 19, 38, 57, 76, 95, 114, 133, 152, 171, 190 |
| 20 | 20, 40, 60, 80, 100, 120, 140, 160, 180, 200 |
1.2 Properties of Multiples
The properties of multiples are given below:
- Every number is a multiple of itself.
For example, the first non-zero multiple of 8 is 8 x 1 = 8
2. The number of multiples of a given number is infinite.
For example, Listing the multiples of 7, we start with: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 …. and so on, since we know that ‘Numbers are infinite’.
3. The multiple of a number is greater than or equal to the number itself (except for 0).
For example, Multiples of 17 are: 17, 34, 51, 68, 85, 102, 119, …
Here all the numbers are greater than or equal to 17.
1.3 Common Multiple
A common multiple is a number that is a shared multiple for the given numbers. In other words, multiples that are common to two numbers are known as common multiples of those numbers. There are infinite common multiples of any set of numbers.
Consider two numbers – 8 and 14. Multiples of 8 and 14 are:
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, …
14: 14, 28, 42, 56, 70, 84, 98, 112, …
Here, 56 is a common multiple of 8 and 14.
