Least Common Multiple of 18 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 18 and 22 the smallest integer that is 198 that is divisible by both numbers.

Least Common Multiple (LCM) of 18 and 22 is 198.

LCM(18,22) = 198

LCM of 18 and 22

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

LCM of:
and

Least Common Multiple of 18 and 22

LCM of 18 and 22 is 198

Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 22. First we will calculate the prime factors of 18 and 22.

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

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 18 and 22.

LCM(18,22) = 21×32×111
LCM(18,22) = 198

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Factors of 22

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

1, 2, 11, 22

Least Common Multiple of 18 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 18 and 22, than apply into the LCM equation.

GCF(18,22) = 2
LCM(18,22) = ( 18 × 22) / 2
LCM(18,22) = 396 / 2
LCM(18,22) = 198

Properties of LCM 18 and 22

(i) The LCM of 22 and 18 is associative

LCM of 18 and 22 = LCM of 22 and 18

Related Least Common Multiples of 18

Related Least Common Multiples of 22

Frequently Asked Questions on LCM of 18 and 22

1. What is the LCM of 18 and 22?

Answer: LCM of 18 and 22 is 198.

2. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

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 18 and 22?

Answer:

Least Common Multiple of 18 and 22 = 198

Step 1: Find the prime factorization of 18

18 = 2 x 3 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 = 198 = 2 x 3 x 3 x 11

Step 4: Therefore, the least common multiple of 18 and 22 is 198.