Least Common Multiple of 10004 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 10004 and 10010 the smallest integer that is 50070020 that is divisible by both numbers.

Least Common Multiple (LCM) of 10004 and 10010 is 50070020.

LCM(10004,10010) = 50070020

LCM of 10004 and 10010

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

LCM of:
and

Least Common Multiple of 10004 and 10010

LCM of 10004 and 10010 is 50070020

Least common multiple can be found by multiplying the highest exponent prime factors of 10004 and 10010. First we will calculate the prime factors of 10004 and 10010.

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 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 10004 and 10010.

LCM(10004,10010) = 22×51×71×111×131×411×611
LCM(10004,10010) = 50070020

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 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 10004 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 10004 and 10010, than apply into the LCM equation.

GCF(10004,10010) = 2
LCM(10004,10010) = ( 10004 × 10010) / 2
LCM(10004,10010) = 100140040 / 2
LCM(10004,10010) = 50070020

Properties of LCM 10004 and 10010

(i) The LCM of 10010 and 10004 is associative

LCM of 10004 and 10010 = LCM of 10010 and 10004

Related Least Common Multiples of 10004

Related Least Common Multiples of 10010

Frequently Asked Questions on LCM of 10004 and 10010

1. What is the LCM of 10004 and 10010?

Answer: LCM of 10004 and 10010 is 50070020.

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 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 10004 and 10010?

Answer:

Least Common Multiple of 10004 and 10010 = 50070020

Step 1: Find the prime factorization of 10004

10004 = 2 x 2 x 41 x 61

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 = 50070020 = 2 x 2 x 5 x 7 x 11 x 13 x 41 x 61

Step 4: Therefore, the least common multiple of 10004 and 10010 is 50070020.