**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 8 and 12?**

LCM of 8 and 12 | 24 |

**LCM of 8 and 12 by Multiples Method**

Find the least common Multiple (LCM) of 8 and 12.

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

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...
```

Multiples of 12

```
12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72
Multiples of 12 are 12, 24, 36, 48, 60, 72...
```

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

Common multiples of 8 and 12 are 24, 48…

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

Least Common Multiple (LCM) = 24 (the smallest number of the common multiples)

**LCM of 8 and 12 by Division Method**

```
2 | 8, 12
--|---------
2 | 4 6
--|---------
2 | 2 3
--|---------
3 | 1 3
--|---------
| 1 1
```

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

LCM = 24

**LCM of 8 and 12 by ****Prime Factorisation** Method

**Prime Factorisation**Method

```
Step 1: Find the prime factorization of 8
2 | 8
--|----
2 | 4
--|----
2 | 2
--|----
| 1
prime factorization of 8 = 2 x 2 x 2
```

```
Step 2: Find the prime factorization of 12
2 | 12
--|-----
2 | 6
--|-----
3 | 3
--|----
| 1
prime factorization of 12 = 2 x 2 x 3
```

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

LCM = 2 x 2 x 2 x 3

LCM = 24

Hence, the LCM of 8 and 12 by prime factorization is 24.