Common Multiple: When two or more numbers have the same numbers as their multiples, those multiples are said to be common multiples.

Least Common Multiple (LCM): The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

**What is the LCM of 6 and 8?**

The LCM of 6 and 8 are 24 |

**LCM of 6 and 8 by Multiples** **Method**

Find the least common Multiple (LCM) of 6 and 8.

Step 1: List the multiples of all the given numbers.

Multiples of 6

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

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

Multiples of 8

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

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

Step 2: Identify the common multipes of all the given numbers.

Common multiples of 6 and 8 are 24…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 20 (the smallest number of the common multiples)

**LCM of 6 and 8 by Division Method**

```
2 | 6 8
--|---------
2 | 3 4
--|---------
2 | 3 2
--|---------
3 | 3 1
--|---------
| 1 1
```

Least Common Multiple (LCM) = 2 x 2 x 2 x 3

LCM = 24

**LCM of 6 and 8 by Prime Factorisation Method**

Step 1: Find the prime factorization of 6

```
2 | 6
--|----
3 | 3
--|----
| 1
```

prime factorization of 6 = 2 x 3

Step 2: Find the prime factorization of 8

```
2 | 8
--|-----
2 | 4
--|-----
2 | 2
--|------
| 1
```

prime factorization of 8 = 2 x 2 x 2

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

6 = 2 x 3

8 = 2 x 2 x 2

LCM = 2 x 2 x 2 x 3

LCM = 24

Hence, the LCM of 6 and 8 by prime factorization is 24.