Least Common Multiple of 10004 and 10008

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 10008 the smallest integer that is 25030008 that is divisible by both numbers.

Least Common Multiple (LCM) of 10004 and 10008 is 25030008.

LCM(10004,10008) = 25030008

LCM of 10004 and 10008

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

LCM of:
and

Least Common Multiple of 10004 and 10008

LCM of 10004 and 10008 is 25030008

Least common multiple can be found by multiplying the highest exponent prime factors of 10004 and 10008. First we will calculate the prime factors of 10004 and 10008.

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 10008


2 10008
2 5004
2 2502
3 1251
3 417
139 139
1

Prime factors of 10008 are 2, 3,139. Prime factorization of 10008 in exponential form is:

10008 = 23×32×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 10004 and 10008.

LCM(10004,10008) = 23×32×411×611×1391
LCM(10004,10008) = 25030008

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 10008

List of positive integer factors of 10008 that divides 10008 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 139, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 5004, 10008

Least Common Multiple of 10004 and 10008 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 10008, than apply into the LCM equation.

GCF(10004,10008) = 4
LCM(10004,10008) = ( 10004 × 10008) / 4
LCM(10004,10008) = 100120032 / 4
LCM(10004,10008) = 25030008

Properties of LCM 10004 and 10008

(i) The LCM of 10008 and 10004 is associative

LCM of 10004 and 10008 = LCM of 10008 and 10004

Related Least Common Multiples of 10004

Related Least Common Multiples of 10008

Frequently Asked Questions on LCM of 10004 and 10008

1. What is the LCM of 10004 and 10008?

Answer: LCM of 10004 and 10008 is 25030008.

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 10008?

Answer: Factors of 10008 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 139, 278, 417, 556, 834, 1112, 1251, 1668, 2502, 3336, 5004, 10008. There are 24 integers that are factors of 10008. The greatest factor of 10008 is 10008.

4. How to Find the LCM of 10004 and 10008?

Answer:

Least Common Multiple of 10004 and 10008 = 25030008

Step 1: Find the prime factorization of 10004

10004 = 2 x 2 x 41 x 61

Step 2: Find the prime factorization of 10008

10008 = 2 x 2 x 2 x 3 x 3 x 139

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

LCM = 25030008 = 2 x 2 x 2 x 3 x 3 x 41 x 61 x 139

Step 4: Therefore, the least common multiple of 10004 and 10008 is 25030008.