Least Common Multiple of 200 and 208

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 208 the smallest integer that is 5200 that is divisible by both numbers.

Least Common Multiple (LCM) of 200 and 208 is 5200.

LCM(200,208) = 5200

LCM of 200 and 208

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

LCM of:
and

Least Common Multiple of 200 and 208

LCM of 200 and 208 is 5200

Least common multiple can be found by multiplying the highest exponent prime factors of 200 and 208. First we will calculate the prime factors of 200 and 208.

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 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

Now multiplying the highest exponent prime factors to calculate the LCM of 200 and 208.

LCM(200,208) = 24×52×131
LCM(200,208) = 5200

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 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208

Least Common Multiple of 200 and 208 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 208, than apply into the LCM equation.

GCF(200,208) = 8
LCM(200,208) = ( 200 × 208) / 8
LCM(200,208) = 41600 / 8
LCM(200,208) = 5200

Properties of LCM 200 and 208

(i) The LCM of 208 and 200 is associative

LCM of 200 and 208 = LCM of 208 and 200

Related Least Common Multiples of 200

Related Least Common Multiples of 208

Frequently Asked Questions on LCM of 200 and 208

1. What is the LCM of 200 and 208?

Answer: LCM of 200 and 208 is 5200.

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 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

4. How to Find the LCM of 200 and 208?

Answer:

Least Common Multiple of 200 and 208 = 5200

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 208

208 = 2 x 2 x 2 x 2 x 13

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

LCM = 5200 = 2 x 2 x 2 x 2 x 5 x 5 x 13

Step 4: Therefore, the least common multiple of 200 and 208 is 5200.