Least Common Multiple of 10000 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 10000 and 10005 the smallest integer that is 20010000 that is divisible by both numbers.

Least Common Multiple (LCM) of 10000 and 10005 is 20010000.

LCM(10000,10005) = 20010000

LCM of 10000 and 10005

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

LCM of:
and

Least Common Multiple of 10000 and 10005

LCM of 10000 and 10005 is 20010000

Least common multiple can be found by multiplying the highest exponent prime factors of 10000 and 10005. First we will calculate the prime factors of 10000 and 10005.

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 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 10000 and 10005.

LCM(10000,10005) = 24×31×54×231×291
LCM(10000,10005) = 20010000

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 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 10000 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 10000 and 10005, than apply into the LCM equation.

GCF(10000,10005) = 5
LCM(10000,10005) = ( 10000 × 10005) / 5
LCM(10000,10005) = 100050000 / 5
LCM(10000,10005) = 20010000

Properties of LCM 10000 and 10005

(i) The LCM of 10005 and 10000 is associative

LCM of 10000 and 10005 = LCM of 10005 and 10000

Related Least Common Multiples of 10000

Related Least Common Multiples of 10005

Frequently Asked Questions on LCM of 10000 and 10005

1. What is the LCM of 10000 and 10005?

Answer: LCM of 10000 and 10005 is 20010000.

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 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 10000 and 10005?

Answer:

Least Common Multiple of 10000 and 10005 = 20010000

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 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 = 20010000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 23 x 29

Step 4: Therefore, the least common multiple of 10000 and 10005 is 20010000.