Least Common Multiple of 200 and 210

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 210 the smallest integer that is 4200 that is divisible by both numbers.

Least Common Multiple (LCM) of 200 and 210 is 4200.

LCM(200,210) = 4200

LCM of 200 and 210

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

LCM of:
and

Least Common Multiple of 200 and 210

LCM of 200 and 210 is 4200

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 210. First we will calculate the prime factors of 200 and 210.

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 210


2 210
3 105
5 35
7 7
1

Prime factors of 210 are 2, 3, 5,7. Prime factorization of 210 in exponential form is:

210 = 21×31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 200 and 210.

LCM(200,210) = 23×31×52×71
LCM(200,210) = 4200

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 210

List of positive integer factors of 210 that divides 210 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

Least Common Multiple of 200 and 210 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 210, than apply into the LCM equation.

GCF(200,210) = 10
LCM(200,210) = ( 200 × 210) / 10
LCM(200,210) = 42000 / 10
LCM(200,210) = 4200

Properties of LCM 200 and 210

(i) The LCM of 210 and 200 is associative

LCM of 200 and 210 = LCM of 210 and 200

Related Least Common Multiples of 200

Related Least Common Multiples of 210

Frequently Asked Questions on LCM of 200 and 210

1. What is the LCM of 200 and 210?

Answer: LCM of 200 and 210 is 4200.

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 210?

Answer: Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. There are 16 integers that are factors of 210. The greatest factor of 210 is 210.

4. How to Find the LCM of 200 and 210?

Answer:

Least Common Multiple of 200 and 210 = 4200

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 210

210 = 2 x 3 x 5 x 7

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

LCM = 4200 = 2 x 2 x 2 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 200 and 210 is 4200.