Least Common Multiple of 200 and 207

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 207 the smallest integer that is 41400 that is divisible by both numbers.

Least Common Multiple (LCM) of 200 and 207 is 41400.

LCM(200,207) = 41400

LCM of 200 and 207

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

LCM of:
and

Least Common Multiple of 200 and 207

LCM of 200 and 207 is 41400

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 207. First we will calculate the prime factors of 200 and 207.

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 207


3 207
3 69
23 23
1

Prime factors of 207 are 3,23. Prime factorization of 207 in exponential form is:

207 = 32×231

Now multiplying the highest exponent prime factors to calculate the LCM of 200 and 207.

LCM(200,207) = 23×32×52×231
LCM(200,207) = 41400

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 207

List of positive integer factors of 207 that divides 207 without a remainder.

1, 3, 9, 23, 69, 207

Least Common Multiple of 200 and 207 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 207, than apply into the LCM equation.

GCF(200,207) = 1
LCM(200,207) = ( 200 × 207) / 1
LCM(200,207) = 41400 / 1
LCM(200,207) = 41400

Properties of LCM 200 and 207

(i) The LCM of 207 and 200 is associative

LCM of 200 and 207 = LCM of 207 and 200

Related Least Common Multiples of 200

Related Least Common Multiples of 207

Frequently Asked Questions on LCM of 200 and 207

1. What is the LCM of 200 and 207?

Answer: LCM of 200 and 207 is 41400.

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 207?

Answer: Factors of 207 are 1, 3, 9, 23, 69, 207. There are 6 integers that are factors of 207. The greatest factor of 207 is 207.

4. How to Find the LCM of 200 and 207?

Answer:

Least Common Multiple of 200 and 207 = 41400

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 207

207 = 3 x 3 x 23

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

LCM = 41400 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 23

Step 4: Therefore, the least common multiple of 200 and 207 is 41400.