Least Common Multiple of 12 and 21

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 21 the smallest integer that is 84 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 21 is 84.

LCM(12,21) = 84

LCM of 12 and 21

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

LCM of:
and

Least Common Multiple of 12 and 21

LCM of 12 and 21 is 84

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 21. First we will calculate the prime factors of 12 and 21.

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 21


3 21
7 7
1

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 21.

LCM(12,21) = 22×31×71
LCM(12,21) = 84

Factors of 12

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

1, 2, 3, 4, 6, 12

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

Least Common Multiple of 12 and 21 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 21, than apply into the LCM equation.

GCF(12,21) = 3
LCM(12,21) = ( 12 × 21) / 3
LCM(12,21) = 252 / 3
LCM(12,21) = 84

Properties of LCM 12 and 21

(i) The LCM of 21 and 12 is associative

LCM of 12 and 21 = LCM of 21 and 12

Related Least Common Multiples of 12

Related Least Common Multiples of 21

Frequently Asked Questions on LCM of 12 and 21

1. What is the LCM of 12 and 21?

Answer: LCM of 12 and 21 is 84.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 12 and 21?

Answer:

Least Common Multiple of 12 and 21 = 84

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

LCM = 84 = 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 12 and 21 is 84.