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.