Least Common Multiple of 5194 and 5200

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5194 and 5200 the smallest integer that is 13504400 that is divisible by both numbers.

Least Common Multiple (LCM) of 5194 and 5200 is 13504400.

LCM(5194,5200) = 13504400

LCM of 5194 and 5200

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

LCM of:
and

Least Common Multiple of 5194 and 5200

LCM of 5194 and 5200 is 13504400

Least common multiple can be found by multiplying the highest exponent prime factors of 5194 and 5200. First we will calculate the prime factors of 5194 and 5200.

Prime Factorization of 5194


2 5194
7 2597
7 371
53 53
1

Prime factors of 5194 are 2, 7,53. Prime factorization of 5194 in exponential form is:

5194 = 21×72×531

Prime Factorization of 5200


2 5200
2 2600
2 1300
2 650
5 325
5 65
13 13
1

Prime factors of 5200 are 2, 5,13. Prime factorization of 5200 in exponential form is:

5200 = 24×52×131

Now multiplying the highest exponent prime factors to calculate the LCM of 5194 and 5200.

LCM(5194,5200) = 24×52×72×131×531
LCM(5194,5200) = 13504400

Factors of 5194

List of positive integer factors of 5194 that divides 5194 without a remainder.

1, 2, 7, 14, 49, 53, 98, 106, 371, 742, 2597, 5194

Factors of 5200

List of positive integer factors of 5200 that divides 5200 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200

Least Common Multiple of 5194 and 5200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5194 and 5200, than apply into the LCM equation.

GCF(5194,5200) = 2
LCM(5194,5200) = ( 5194 × 5200) / 2
LCM(5194,5200) = 27008800 / 2
LCM(5194,5200) = 13504400

Properties of LCM 5194 and 5200

(i) The LCM of 5200 and 5194 is associative

LCM of 5194 and 5200 = LCM of 5200 and 5194

Related Least Common Multiples of 5194

Related Least Common Multiples of 5200

Frequently Asked Questions on LCM of 5194 and 5200

1. What is the LCM of 5194 and 5200?

Answer: LCM of 5194 and 5200 is 13504400.

2. What are the Factors of 5194?

Answer: Factors of 5194 are 1, 2, 7, 14, 49, 53, 98, 106, 371, 742, 2597, 5194. There are 12 integers that are factors of 5194. The greatest factor of 5194 is 5194.

3. What are the Factors of 5200?

Answer: Factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200. There are 30 integers that are factors of 5200. The greatest factor of 5200 is 5200.

4. How to Find the LCM of 5194 and 5200?

Answer:

Least Common Multiple of 5194 and 5200 = 13504400

Step 1: Find the prime factorization of 5194

5194 = 2 x 7 x 7 x 53

Step 2: Find the prime factorization of 5200

5200 = 2 x 2 x 2 x 2 x 5 x 5 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 = 13504400 = 2 x 2 x 2 x 2 x 5 x 5 x 7 x 7 x 13 x 53

Step 4: Therefore, the least common multiple of 5194 and 5200 is 13504400.