Least Common Multiple of 5200 and 5205

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5200 and 5205 the smallest integer that is 5413200 that is divisible by both numbers.

Least Common Multiple (LCM) of 5200 and 5205 is 5413200.

LCM(5200,5205) = 5413200

LCM of 5200 and 5205

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

LCM of:
and

Least Common Multiple of 5200 and 5205

LCM of 5200 and 5205 is 5413200

Least common multiple can be found by multiplying the highest exponent prime factors of 5200 and 5205. First we will calculate the prime factors of 5200 and 5205.

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

Prime Factorization of 5205


3 5205
5 1735
347 347
1

Prime factors of 5205 are 3, 5,347. Prime factorization of 5205 in exponential form is:

5205 = 31×51×3471

Now multiplying the highest exponent prime factors to calculate the LCM of 5200 and 5205.

LCM(5200,5205) = 24×31×52×131×3471
LCM(5200,5205) = 5413200

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

Factors of 5205

List of positive integer factors of 5205 that divides 5205 without a remainder.

1, 3, 5, 15, 347, 1041, 1735, 5205

Least Common Multiple of 5200 and 5205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5200 and 5205, than apply into the LCM equation.

GCF(5200,5205) = 5
LCM(5200,5205) = ( 5200 × 5205) / 5
LCM(5200,5205) = 27066000 / 5
LCM(5200,5205) = 5413200

Properties of LCM 5200 and 5205

(i) The LCM of 5205 and 5200 is associative

LCM of 5200 and 5205 = LCM of 5205 and 5200

Related Least Common Multiples of 5200

Related Least Common Multiples of 5205

Frequently Asked Questions on LCM of 5200 and 5205

1. What is the LCM of 5200 and 5205?

Answer: LCM of 5200 and 5205 is 5413200.

2. 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.

3. What are the Factors of 5205?

Answer: Factors of 5205 are 1, 3, 5, 15, 347, 1041, 1735, 5205. There are 8 integers that are factors of 5205. The greatest factor of 5205 is 5205.

4. How to Find the LCM of 5200 and 5205?

Answer:

Least Common Multiple of 5200 and 5205 = 5413200

Step 1: Find the prime factorization of 5200

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

Step 2: Find the prime factorization of 5205

5205 = 3 x 5 x 347

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

LCM = 5413200 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13 x 347

Step 4: Therefore, the least common multiple of 5200 and 5205 is 5413200.