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 4 and 12?**

The LCM of 4 and 12 is 12 |

**LCM of 4 and 12 by Multiples** **Method**

Find the least common Multiple (LCM) of 4 and 10.

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

Multiples of 4

4 x 1 = 4

4 x 2 = 8

4 x 3 = 12

4 x 4 = 16

4 x 5 = 20

4 x 6 = 24

Multiples of 4 are 4, 8, 12, 16, 20, 24…

Multiples of 10

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 4 and 12 are 12…

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

Least Common Multiple (LCM) = 12 (the smallest number of the common multiples)

**LCM of 4 and 12 by Division Method**

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

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

LCM = 12

LCM of 4 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 4

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

prime factorization of 4 = 2 x 2

Step 2: Find the prime factorization of 10

```
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

4 = 2 x 2

10 = 2 x 2 x 3

LCM = 2 x 2 x 3

LCM = 12

Hence, the LCM of 4 and 12 by prime factorization is 12.