Least Common Multiple of 10004 and 10005

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10004 and 10005 the smallest integer that is 100090020 that is divisible by both numbers.

Least Common Multiple (LCM) of 10004 and 10005 is 100090020.

LCM(10004,10005) = 100090020

LCM of 10004 and 10005

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

LCM of:
and

Least Common Multiple of 10004 and 10005

LCM of 10004 and 10005 is 100090020

Least common multiple can be found by multiplying the highest exponent prime factors of 10004 and 10005. First we will calculate the prime factors of 10004 and 10005.

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

Prime Factorization of 10005


3 10005
5 3335
23 667
29 29
1

Prime factors of 10005 are 3, 5, 23,29. Prime factorization of 10005 in exponential form is:

10005 = 31×51×231×291

Now multiplying the highest exponent prime factors to calculate the LCM of 10004 and 10005.

LCM(10004,10005) = 22×31×51×231×291×411×611
LCM(10004,10005) = 100090020

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

Factors of 10005

List of positive integer factors of 10005 that divides 10005 without a remainder.

1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005

Least Common Multiple of 10004 and 10005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10004 and 10005, than apply into the LCM equation.

GCF(10004,10005) = 1
LCM(10004,10005) = ( 10004 × 10005) / 1
LCM(10004,10005) = 100090020 / 1
LCM(10004,10005) = 100090020

Properties of LCM 10004 and 10005

(i) The LCM of 10005 and 10004 is associative

LCM of 10004 and 10005 = LCM of 10005 and 10004

Related Least Common Multiples of 10004

Related Least Common Multiples of 10005

Frequently Asked Questions on LCM of 10004 and 10005

1. What is the LCM of 10004 and 10005?

Answer: LCM of 10004 and 10005 is 100090020.

2. 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.

3. What are the Factors of 10005?

Answer: Factors of 10005 are 1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005. There are 16 integers that are factors of 10005. The greatest factor of 10005 is 10005.

4. How to Find the LCM of 10004 and 10005?

Answer:

Least Common Multiple of 10004 and 10005 = 100090020

Step 1: Find the prime factorization of 10004

10004 = 2 x 2 x 41 x 61

Step 2: Find the prime factorization of 10005

10005 = 3 x 5 x 23 x 29

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

LCM = 100090020 = 2 x 2 x 3 x 5 x 23 x 29 x 41 x 61

Step 4: Therefore, the least common multiple of 10004 and 10005 is 100090020.