LCM of 4 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 4 and 12?

The LCM of 4 and 12 is 12

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)

    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.