Least Common Multiple of 200 and 206

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 206 the smallest integer that is 20600 that is divisible by both numbers.

Least Common Multiple (LCM) of 200 and 206 is 20600.

LCM(200,206) = 20600

LCM of 200 and 206

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

LCM of:
and

Least Common Multiple of 200 and 206

LCM of 200 and 206 is 20600

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 206. First we will calculate the prime factors of 200 and 206.

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 206


2 206
103 103
1

Prime factors of 206 are 2,103. Prime factorization of 206 in exponential form is:

206 = 21×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 200 and 206.

LCM(200,206) = 23×52×1031
LCM(200,206) = 20600

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 206

List of positive integer factors of 206 that divides 206 without a remainder.

1, 2, 103, 206

Least Common Multiple of 200 and 206 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 206, than apply into the LCM equation.

GCF(200,206) = 2
LCM(200,206) = ( 200 × 206) / 2
LCM(200,206) = 41200 / 2
LCM(200,206) = 20600

Properties of LCM 200 and 206

(i) The LCM of 206 and 200 is associative

LCM of 200 and 206 = LCM of 206 and 200

Related Least Common Multiples of 200

Related Least Common Multiples of 206

Frequently Asked Questions on LCM of 200 and 206

1. What is the LCM of 200 and 206?

Answer: LCM of 200 and 206 is 20600.

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 206?

Answer: Factors of 206 are 1, 2, 103, 206. There are 4 integers that are factors of 206. The greatest factor of 206 is 206.

4. How to Find the LCM of 200 and 206?

Answer:

Least Common Multiple of 200 and 206 = 20600

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 206

206 = 2 x 103

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

LCM = 20600 = 2 x 2 x 2 x 5 x 5 x 103

Step 4: Therefore, the least common multiple of 200 and 206 is 20600.