Least Common Multiple of 198 and 204

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 198 and 204 the smallest integer that is 6732 that is divisible by both numbers.

Least Common Multiple (LCM) of 198 and 204 is 6732.

LCM(198,204) = 6732

LCM of 198 and 204

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

LCM of:
and

Least Common Multiple of 198 and 204

LCM of 198 and 204 is 6732

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 204. First we will calculate the prime factors of 198 and 204.

Prime Factorization of 198


2 198
3 99
3 33
11 11
1

Prime factors of 198 are 2, 3,11. Prime factorization of 198 in exponential form is:

198 = 21×32×111

Prime Factorization of 204


2 204
2 102
3 51
17 17
1

Prime factors of 204 are 2, 3,17. Prime factorization of 204 in exponential form is:

204 = 22×31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 204.

LCM(198,204) = 22×32×111×171
LCM(198,204) = 6732

Factors of 198

List of positive integer factors of 198 that divides 198 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

Least Common Multiple of 198 and 204 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 198 and 204, than apply into the LCM equation.

GCF(198,204) = 6
LCM(198,204) = ( 198 × 204) / 6
LCM(198,204) = 40392 / 6
LCM(198,204) = 6732

Properties of LCM 198 and 204

(i) The LCM of 204 and 198 is associative

LCM of 198 and 204 = LCM of 204 and 198

Related Least Common Multiples of 198

Related Least Common Multiples of 204

Frequently Asked Questions on LCM of 198 and 204

1. What is the LCM of 198 and 204?

Answer: LCM of 198 and 204 is 6732.

2. What are the Factors of 198?

Answer: Factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. There are 12 integers that are factors of 198. The greatest factor of 198 is 198.

3. What are the Factors of 204?

Answer: Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. There are 12 integers that are factors of 204. The greatest factor of 204 is 204.

4. How to Find the LCM of 198 and 204?

Answer:

Least Common Multiple of 198 and 204 = 6732

Step 1: Find the prime factorization of 198

198 = 2 x 3 x 3 x 11

Step 2: Find the prime factorization of 204

204 = 2 x 2 x 3 x 17

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

LCM = 6732 = 2 x 2 x 3 x 3 x 11 x 17

Step 4: Therefore, the least common multiple of 198 and 204 is 6732.