Least Common Multiple of 12 and 22

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12 and 22 the smallest integer that is 132 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 22 is 132.

LCM(12,22) = 132

LCM of 12 and 22

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 12 and 22

LCM of 12 and 22 is 132

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 22. First we will calculate the prime factors of 12 and 22.

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Prime Factorization of 22


2 22
11 11
1

Prime factors of 22 are 2,11. Prime factorization of 22 in exponential form is:

22 = 21×111

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 22.

LCM(12,22) = 22×31×111
LCM(12,22) = 132

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 22

List of positive integer factors of 22 that divides 22 without a remainder.

1, 2, 11, 22

Least Common Multiple of 12 and 22 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 22, than apply into the LCM equation.

GCF(12,22) = 2
LCM(12,22) = ( 12 × 22) / 2
LCM(12,22) = 264 / 2
LCM(12,22) = 132

Properties of LCM 12 and 22

(i) The LCM of 22 and 12 is associative

LCM of 12 and 22 = LCM of 22 and 12

Related Least Common Multiples of 12

Related Least Common Multiples of 22

Frequently Asked Questions on LCM of 12 and 22

1. What is the LCM of 12 and 22?

Answer: LCM of 12 and 22 is 132.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 22?

Answer: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22.

4. How to Find the LCM of 12 and 22?

Answer:

Least Common Multiple of 12 and 22 = 132

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 22

22 = 2 x 11

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 132 = 2 x 2 x 3 x 11

Step 4: Therefore, the least common multiple of 12 and 22 is 132.