LCM of 6 and 8

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 6 and 8?

The LCM of 6 and 8 are 24

Find the least common Multiple (LCM) of 6 and 8.

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

Multiples of 6

6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30
6 x 6 = 36

Multiples of 6 are 6, 12, 18, 24, 30, 36…

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…

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

Common multiples of 6 and 8 are 24…

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

Least Common Multiple (LCM) = 20 (the smallest number of the common multiples)

   2 | 6  8
   --|---------
   2 | 3  4
   --|---------
   2 | 3  2
   --|---------
   3 | 3  1
   --|---------
      | 1  1

Least Common Multiple (LCM) = 2 x 2 x 2 x 3
LCM = 24

Step 1: Find the prime factorization of 6

  2 | 6
  --|---- 
  3 | 3
  --|----
     | 1

prime factorization of 6 = 2 x 3

Step 2: Find the prime factorization of 8

   2 | 8
   --|----- 
   2 | 4
   --|-----
   2 | 2
   --|------
      | 1

prime factorization of 8 = 2 x 2 x 2

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

6 = 2 x 3

8 = 2 x 2 x 2

LCM = 2 x 2 x 2 x 3
LCM = 24

Hence, the LCM of 6 and 8 by prime factorization is 24.