# Multiples Calculator

## What is a multiple in math?

The multiple of a number is the product of this number by any other number (0, 1, 2, 3, ...).

Our calculator works on the set of natural numbers, but there are multiples in the set of numbers, integers, real, etc. Therefore, a multiple can also be negative.

For example, the number 9 can be divided by 3 without a reminder. Like this, 9 is a multiple of 3, because, 3 times 3 equals 9. In other words, we can say that 9 is a multiple of 3 because there is a natural - 3 - which multiplied by 3 equals 9. The statement '9 is a multiple of 3' is equivalent '9 is divisible by 3', or that 3 is a divider of 9.

So to find the multiples of 3, simply multiply this number by a number of the set of natural numbers as many times as we want. See below how to do it for the number 3:

- 3 x 0 = 0 so, 0 is a multiple of 3.
- 3 x 1 = 3 so, 3 is a multiple of 3.
- 3 x 2 = 6 so, 6 is a multiple of 3.
- 3 x 3 = 9 so, 9 is a multiple of 3.
- 3 x 4 = 12 so, 12 is a multiple of 3.
- 3 x 5 = 15 so, 15 is a multiple of 3.
- 3 x 6 = 18 so, 18 is a multiple of 3.

The first 7 multiples of 3 are: 0, 3, 6, 9, 12, 15, 18.

## Facts About Multiples

- Any number is a multiple of itself (n x 1 = n).
- Any number is a multiple of 1 (1 x n = n).
- Zero is a multiple of any number (0 x n = 0).
- The set of multiples of a number is an infinite set, since we can get this by multiplying the number given by all natural numbers. The set of multiples of n can be represented by M

_{n}= {0 x n, 1 x n, 2 x n, 3 x n, 4 x n, ...} (where n is any natural). For example, the set of multiples of 3 is represented as M

_{3 = {0, 3,6,9,12, ...}. }

## Common Multiples

If two numbers are multiplied, then the product is a common multiple of these two numbers.

Example: if two numbers 3 and 3 are multiplied, then the result 9 is a common multiple of 3 and 3.

Note: The product of these two numbers is not necessarily the least common multiple-LCM of these numbers.

## Multiples Table

- 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
- 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
- 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60
- 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80
- 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
- 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120
- 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140
- 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160
- 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180
- 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200
- 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220
- 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240
- 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260
- 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280
- 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300