Least Common Multiple of 200 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 200 and 204 the smallest integer that is 10200 that is divisible by both numbers.

Least Common Multiple (LCM) of 200 and 204 is 10200.

LCM(200,204) = 10200

LCM of 200 and 204

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

LCM of:
and

Least Common Multiple of 200 and 204

LCM of 200 and 204 is 10200

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 204. First we will calculate the prime factors of 200 and 204.

Prime Factorization of 200


2 200
2 100
2 50
5 25
5 5
1

Prime factors of 200 are 2,5. Prime factorization of 200 in exponential form is:

200 = 23×52

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 200 and 204.

LCM(200,204) = 23×31×52×171
LCM(200,204) = 10200

Factors of 200

List of positive integer factors of 200 that divides 200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

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 200 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 200 and 204, than apply into the LCM equation.

GCF(200,204) = 4
LCM(200,204) = ( 200 × 204) / 4
LCM(200,204) = 40800 / 4
LCM(200,204) = 10200

Properties of LCM 200 and 204

(i) The LCM of 204 and 200 is associative

LCM of 200 and 204 = LCM of 204 and 200

Related Least Common Multiples of 200

Related Least Common Multiples of 204

Frequently Asked Questions on LCM of 200 and 204

1. What is the LCM of 200 and 204?

Answer: LCM of 200 and 204 is 10200.

2. What are the Factors of 200?

Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.

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 200 and 204?

Answer:

Least Common Multiple of 200 and 204 = 10200

Step 1: Find the prime factorization of 200

200 = 2 x 2 x 2 x 5 x 5

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 = 10200 = 2 x 2 x 2 x 3 x 5 x 5 x 17

Step 4: Therefore, the least common multiple of 200 and 204 is 10200.