LCM of 7 and 12

LCM is 84 for 7 and 12. In mathematics, the value that is evenly divisible by any two integers is known as their LCM.

The LCM of 7 and 12 is the smallest number among all frequent multiples of 7 and 12. The first few multiples of 7 and 12 are (7, 14, 21, 28,…) and (12, 24, 36, 48, 60, 72, 84,…).

Three common approaches—listing multiples, the division technique, and prime factorization—can be used to get the LCM of 7 and 12.

LCM of 7 and 12 means

This question’s response is 84. This article illustrates the LCM of 7 and 12 using several techniques. The smallest positive number 84 that is evenly divided by both 7 and 12 and leaves no remainder is the LCM of two non-zero integers, 7, 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 7 and 12?

LCM of 7 and 12 with Multiples

Find the least common Multiple (LCM) of 7 and 12.

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

Multiples of 7

7 x 1 = 7
7 x 2 = 14
7 x 3 = 21
7 x 4 = 28
7 x 5 = 35
7 x 6 = 42
7 x 7 = 49
7 x 8 = 56
7 x 9 = 63
7 x 10 = 70
7 x 11 = 77
7 x 12 = 84
7 x 13 = 91

Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91…

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
12 x 7 = 84
12 x 8 = 96
12 x 9 = 108

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108…

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

Common multiples of 7 and 12 are 84…

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

Least Common Multiple (LCM) = 84 (the smallest number of the common multiples)

LCM of 7 and 12 by Division Method

   2| 7  12
  --|---------
   2| 7  6
  --|---------
   3| 7  3
  --|---------
   7| 7  1
  --|---------
    | 1  1

Least Common Multiple (LCM) = 2 x 2 x 3 x 7
LCM = 84

LCM of 7 and 12 by Prime Factorisation Method

Step 1: Find the prime factorization of 7

   7| 7
  --|---- 
    | 1

prime factorization of 7 = 7

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

7 = 7

12 = 2 x 2 x 3

LCM = 2 x 2 x 3 x 7
LCM = 84

Hence, the LCM of 7 and 12 by prime factorization is 84.