Least Common Multiple of 10005 and 10010

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10005 and 10010 the smallest integer that is 20030010 that is divisible by both numbers.

Least Common Multiple (LCM) of 10005 and 10010 is 20030010.

LCM(10005,10010) = 20030010

LCM of 10005 and 10010

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

LCM of:
and

Least Common Multiple of 10005 and 10010

LCM of 10005 and 10010 is 20030010

Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10010. First we will calculate the prime factors of 10005 and 10010.

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

Prime Factorization of 10010


2 10010
5 5005
7 1001
11 143
13 13
1

Prime factors of 10010 are 2, 5, 7, 11,13. Prime factorization of 10010 in exponential form is:

10010 = 21×51×71×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 10005 and 10010.

LCM(10005,10010) = 21×31×51×71×111×131×231×291
LCM(10005,10010) = 20030010

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

Factors of 10010

List of positive integer factors of 10010 that divides 10010 without a remainder.

1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010

Least Common Multiple of 10005 and 10010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10005 and 10010, than apply into the LCM equation.

GCF(10005,10010) = 5
LCM(10005,10010) = ( 10005 × 10010) / 5
LCM(10005,10010) = 100150050 / 5
LCM(10005,10010) = 20030010

Properties of LCM 10005 and 10010

(i) The LCM of 10010 and 10005 is associative

LCM of 10005 and 10010 = LCM of 10010 and 10005

Related Least Common Multiples of 10005

Related Least Common Multiples of 10010

Frequently Asked Questions on LCM of 10005 and 10010

1. What is the LCM of 10005 and 10010?

Answer: LCM of 10005 and 10010 is 20030010.

2. 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.

3. What are the Factors of 10010?

Answer: Factors of 10010 are 1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005, 10010. There are 32 integers that are factors of 10010. The greatest factor of 10010 is 10010.

4. How to Find the LCM of 10005 and 10010?

Answer:

Least Common Multiple of 10005 and 10010 = 20030010

Step 1: Find the prime factorization of 10005

10005 = 3 x 5 x 23 x 29

Step 2: Find the prime factorization of 10010

10010 = 2 x 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 = 20030010 = 2 x 3 x 5 x 7 x 11 x 13 x 23 x 29

Step 4: Therefore, the least common multiple of 10005 and 10010 is 20030010.