Least Common Multiple of 200 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 200 and 205 the smallest integer that is 8200 that is divisible by both numbers.

Least Common Multiple (LCM) of 200 and 205 is 8200.

LCM(200,205) = 8200

LCM of 200 and 205

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

LCM of:
and

Least Common Multiple of 200 and 205

LCM of 200 and 205 is 8200

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 205. First we will calculate the prime factors of 200 and 205.

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 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 200 and 205.

LCM(200,205) = 23×52×411
LCM(200,205) = 8200

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 205

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

1, 5, 41, 205

Least Common Multiple of 200 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 200 and 205, than apply into the LCM equation.

GCF(200,205) = 5
LCM(200,205) = ( 200 × 205) / 5
LCM(200,205) = 41000 / 5
LCM(200,205) = 8200

Properties of LCM 200 and 205

(i) The LCM of 205 and 200 is associative

LCM of 200 and 205 = LCM of 205 and 200

Related Least Common Multiples of 200

Related Least Common Multiples of 205

Frequently Asked Questions on LCM of 200 and 205

1. What is the LCM of 200 and 205?

Answer: LCM of 200 and 205 is 8200.

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 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 200 and 205?

Answer:

Least Common Multiple of 200 and 205 = 8200

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 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 = 8200 = 2 x 2 x 2 x 5 x 5 x 41

Step 4: Therefore, the least common multiple of 200 and 205 is 8200.