Least Common Multiple of 21 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 21 and 22 the smallest integer that is 462 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 22 is 462.

LCM(21,22) = 462

LCM of 21 and 22

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

LCM of:
and

Least Common Multiple of 21 and 22

LCM of 21 and 22 is 462

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 22. First we will calculate the prime factors of 21 and 22.

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

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 21 and 22.

LCM(21,22) = 21×31×71×111
LCM(21,22) = 462

Factors of 21

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

1, 3, 7, 21

Factors of 22

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

1, 2, 11, 22

Least Common Multiple of 21 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 21 and 22, than apply into the LCM equation.

GCF(21,22) = 1
LCM(21,22) = ( 21 × 22) / 1
LCM(21,22) = 462 / 1
LCM(21,22) = 462

Properties of LCM 21 and 22

(i) The LCM of 22 and 21 is associative

LCM of 21 and 22 = LCM of 22 and 21

Related Least Common Multiples of 21

Related Least Common Multiples of 22

Frequently Asked Questions on LCM of 21 and 22

1. What is the LCM of 21 and 22?

Answer: LCM of 21 and 22 is 462.

2. 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.

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 21 and 22?

Answer:

Least Common Multiple of 21 and 22 = 462

Step 1: Find the prime factorization of 21

21 = 3 x 7

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 = 462 = 2 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 21 and 22 is 462.