Least Common Multiple of 204 and 205

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 204 and 205 the smallest integer that is 41820 that is divisible by both numbers.

Least Common Multiple (LCM) of 204 and 205 is 41820.

LCM(204,205) = 41820

LCM of 204 and 205

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

LCM of:
and

Least Common Multiple of 204 and 205

LCM of 204 and 205 is 41820

Least common multiple can be found by multiplying the highest exponent prime factors of 204 and 205. First we will calculate the prime factors of 204 and 205.

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

Prime Factorization of 205


5 205
41 41
1

Prime factors of 205 are 5,41. Prime factorization of 205 in exponential form is:

205 = 51×411

Now multiplying the highest exponent prime factors to calculate the LCM of 204 and 205.

LCM(204,205) = 22×31×51×171×411
LCM(204,205) = 41820

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

Factors of 205

List of positive integer factors of 205 that divides 205 without a remainder.

1, 5, 41, 205

Least Common Multiple of 204 and 205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 204 and 205, than apply into the LCM equation.

GCF(204,205) = 1
LCM(204,205) = ( 204 × 205) / 1
LCM(204,205) = 41820 / 1
LCM(204,205) = 41820

Properties of LCM 204 and 205

(i) The LCM of 205 and 204 is associative

LCM of 204 and 205 = LCM of 205 and 204

Related Least Common Multiples of 204

Related Least Common Multiples of 205

Frequently Asked Questions on LCM of 204 and 205

1. What is the LCM of 204 and 205?

Answer: LCM of 204 and 205 is 41820.

2. 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.

3. What are the Factors of 205?

Answer: Factors of 205 are 1, 5, 41, 205. There are 4 integers that are factors of 205. The greatest factor of 205 is 205.

4. How to Find the LCM of 204 and 205?

Answer:

Least Common Multiple of 204 and 205 = 41820

Step 1: Find the prime factorization of 204

204 = 2 x 2 x 3 x 17

Step 2: Find the prime factorization of 205

205 = 5 x 41

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

LCM = 41820 = 2 x 2 x 3 x 5 x 17 x 41

Step 4: Therefore, the least common multiple of 204 and 205 is 41820.