# LCM of 8 and 12

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 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

``````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.

Categories LCM