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 9 and 12?**

The LCM of 9 and 12 is 36 |

**LCM of 9 and 12 with Multiples**

Find the least common Multiple (LCM) of 9 and 12.

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

Multiples of 9

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

9 x 6 = 54

Multiples of 9 are 9, 18, 27, 36, 45, 54…

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 multiples of all the given numbers.

Common multiples of 9 and 12 are 36…

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

Least Common Multiple (LCM) = 36 (the smallest number of the common multiples)

**LCM of 9 and 12 by Division Method**

```
2| 9 12
--|---------
2| 9 6
--|---------
3| 9 3
--|---------
3| 3 1
--|---------
| 1 1
```

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

LCM = 36

LCM of 9 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 9

```
3| 9
--|----
3| 3
--|----
| 1
```

prime factorization of 9 = 3 x 3

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

9 = 3 x 3

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 3

LCM = 36

Hence, the LCM of 9 and 12 by prime factorization is 36.