Least Common Multiple of 9 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 9 and 22 the smallest integer that is 198 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 22 is 198.

LCM(9,22) = 198

LCM of 9 and 22

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

LCM of:
and

Least Common Multiple of 9 and 22

LCM of 9 and 22 is 198

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 22. First we will calculate the prime factors of 9 and 22.

Prime Factorization of 9


3 9
3 3
1

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 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 9 and 22.

LCM(9,22) = 21×32×111
LCM(9,22) = 198

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

Factors of 22

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

1, 2, 11, 22

Least Common Multiple of 9 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 9 and 22, than apply into the LCM equation.

GCF(9,22) = 1
LCM(9,22) = ( 9 × 22) / 1
LCM(9,22) = 198 / 1
LCM(9,22) = 198

Properties of LCM 9 and 22

(i) The LCM of 22 and 9 is associative

LCM of 9 and 22 = LCM of 22 and 9

Frequently Asked Questions on LCM of 9 and 22

1. What is the LCM of 9 and 22?

Answer: LCM of 9 and 22 is 198.

2. What are the Factors of 9?

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

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 9 and 22?

Answer:

Least Common Multiple of 9 and 22 = 198

Step 1: Find the prime factorization of 9

9 = 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 9 and 22 is 198.