Least Common Multiple of 5000 and 5005

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5000 and 5005 the smallest integer that is 5005000 that is divisible by both numbers.

Least Common Multiple (LCM) of 5000 and 5005 is 5005000.

LCM(5000,5005) = 5005000

LCM of 5000 and 5005

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

LCM of:
and

Least Common Multiple of 5000 and 5005

LCM of 5000 and 5005 is 5005000

Least common multiple can be found by multiplying the highest exponent prime factors of 5000 and 5005. First we will calculate the prime factors of 5000 and 5005.

Prime Factorization of 5000


2 5000
2 2500
2 1250
5 625
5 125
5 25
5 5
1

Prime factors of 5000 are 2,5. Prime factorization of 5000 in exponential form is:

5000 = 23×54

Prime Factorization of 5005


5 5005
7 1001
11 143
13 13
1

Prime factors of 5005 are 5, 7, 11,13. Prime factorization of 5005 in exponential form is:

5005 = 51×71×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 5000 and 5005.

LCM(5000,5005) = 23×54×71×111×131
LCM(5000,5005) = 5005000

Factors of 5000

List of positive integer factors of 5000 that divides 5000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000

Factors of 5005

List of positive integer factors of 5005 that divides 5005 without a remainder.

1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005

Least Common Multiple of 5000 and 5005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5000 and 5005, than apply into the LCM equation.

GCF(5000,5005) = 5
LCM(5000,5005) = ( 5000 × 5005) / 5
LCM(5000,5005) = 25025000 / 5
LCM(5000,5005) = 5005000

Properties of LCM 5000 and 5005

(i) The LCM of 5005 and 5000 is associative

LCM of 5000 and 5005 = LCM of 5005 and 5000

Related Least Common Multiples of 5000

Related Least Common Multiples of 5005

Frequently Asked Questions on LCM of 5000 and 5005

1. What is the LCM of 5000 and 5005?

Answer: LCM of 5000 and 5005 is 5005000.

2. What are the Factors of 5000?

Answer: Factors of 5000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000. There are 20 integers that are factors of 5000. The greatest factor of 5000 is 5000.

3. What are the Factors of 5005?

Answer: Factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005. There are 16 integers that are factors of 5005. The greatest factor of 5005 is 5005.

4. How to Find the LCM of 5000 and 5005?

Answer:

Least Common Multiple of 5000 and 5005 = 5005000

Step 1: Find the prime factorization of 5000

5000 = 2 x 2 x 2 x 5 x 5 x 5 x 5

Step 2: Find the prime factorization of 5005

5005 = 5 x 7 x 11 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 = 5005000 = 2 x 2 x 2 x 5 x 5 x 5 x 5 x 7 x 11 x 13

Step 4: Therefore, the least common multiple of 5000 and 5005 is 5005000.