Least Common Multiple of 5200 and 5208

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 5208 the smallest integer that is 3385200 that is divisible by both numbers.

Least Common Multiple (LCM) of 5200 and 5208 is 3385200.

LCM(5200,5208) = 3385200

LCM of 5200 and 5208

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

LCM of:
and

Least Common Multiple of 5200 and 5208

LCM of 5200 and 5208 is 3385200

Least common multiple can be found by multiplying the highest exponent prime factors of 5200 and 5208. First we will calculate the prime factors of 5200 and 5208.

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 5208


2 5208
2 2604
2 1302
3 651
7 217
31 31
1

Prime factors of 5208 are 2, 3, 7,31. Prime factorization of 5208 in exponential form is:

5208 = 23×31×71×311

Now multiplying the highest exponent prime factors to calculate the LCM of 5200 and 5208.

LCM(5200,5208) = 24×31×52×71×131×311
LCM(5200,5208) = 3385200

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 5208

List of positive integer factors of 5208 that divides 5208 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 31, 42, 56, 62, 84, 93, 124, 168, 186, 217, 248, 372, 434, 651, 744, 868, 1302, 1736, 2604, 5208

Least Common Multiple of 5200 and 5208 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 5208, than apply into the LCM equation.

GCF(5200,5208) = 8
LCM(5200,5208) = ( 5200 × 5208) / 8
LCM(5200,5208) = 27081600 / 8
LCM(5200,5208) = 3385200

Properties of LCM 5200 and 5208

(i) The LCM of 5208 and 5200 is associative

LCM of 5200 and 5208 = LCM of 5208 and 5200

Related Least Common Multiples of 5200

Related Least Common Multiples of 5208

Frequently Asked Questions on LCM of 5200 and 5208

1. What is the LCM of 5200 and 5208?

Answer: LCM of 5200 and 5208 is 3385200.

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 5208?

Answer: Factors of 5208 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 31, 42, 56, 62, 84, 93, 124, 168, 186, 217, 248, 372, 434, 651, 744, 868, 1302, 1736, 2604, 5208. There are 32 integers that are factors of 5208. The greatest factor of 5208 is 5208.

4. How to Find the LCM of 5200 and 5208?

Answer:

Least Common Multiple of 5200 and 5208 = 3385200

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 5208

5208 = 2 x 2 x 2 x 3 x 7 x 31

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

LCM = 3385200 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 13 x 31

Step 4: Therefore, the least common multiple of 5200 and 5208 is 3385200.