Least Common Multiple of 10000 and 10004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10000 and 10004 the smallest integer that is 25010000 that is divisible by both numbers.

Least Common Multiple (LCM) of 10000 and 10004 is 25010000.

LCM(10000,10004) = 25010000

LCM of 10000 and 10004

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

LCM of:
and

Least Common Multiple of 10000 and 10004

LCM of 10000 and 10004 is 25010000

Least common multiple can be found by multiplying the highest exponent prime factors of 10000 and 10004. First we will calculate the prime factors of 10000 and 10004.

Prime Factorization of 10000


2 10000
2 5000
2 2500
2 1250
5 625
5 125
5 25
5 5
1

Prime factors of 10000 are 2,5. Prime factorization of 10000 in exponential form is:

10000 = 24×54

Prime Factorization of 10004


2 10004
2 5002
41 2501
61 61
1

Prime factors of 10004 are 2, 41,61. Prime factorization of 10004 in exponential form is:

10004 = 22×411×611

Now multiplying the highest exponent prime factors to calculate the LCM of 10000 and 10004.

LCM(10000,10004) = 24×54×411×611
LCM(10000,10004) = 25010000

Factors of 10000

List of positive integer factors of 10000 that divides 10000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000

Factors of 10004

List of positive integer factors of 10004 that divides 10004 without a remainder.

1, 2, 4, 41, 61, 82, 122, 164, 244, 2501, 5002, 10004

Least Common Multiple of 10000 and 10004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10000 and 10004, than apply into the LCM equation.

GCF(10000,10004) = 4
LCM(10000,10004) = ( 10000 × 10004) / 4
LCM(10000,10004) = 100040000 / 4
LCM(10000,10004) = 25010000

Properties of LCM 10000 and 10004

(i) The LCM of 10004 and 10000 is associative

LCM of 10000 and 10004 = LCM of 10004 and 10000

Related Least Common Multiples of 10000

Related Least Common Multiples of 10004

Frequently Asked Questions on LCM of 10000 and 10004

1. What is the LCM of 10000 and 10004?

Answer: LCM of 10000 and 10004 is 25010000.

2. What are the Factors of 10000?

Answer: Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000. There are 25 integers that are factors of 10000. The greatest factor of 10000 is 10000.

3. What are the Factors of 10004?

Answer: Factors of 10004 are 1, 2, 4, 41, 61, 82, 122, 164, 244, 2501, 5002, 10004. There are 12 integers that are factors of 10004. The greatest factor of 10004 is 10004.

4. How to Find the LCM of 10000 and 10004?

Answer:

Least Common Multiple of 10000 and 10004 = 25010000

Step 1: Find the prime factorization of 10000

10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5

Step 2: Find the prime factorization of 10004

10004 = 2 x 2 x 41 x 61

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

LCM = 25010000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 41 x 61

Step 4: Therefore, the least common multiple of 10000 and 10004 is 25010000.