Least Common Multiple of 10006 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 10006 and 10008 the smallest integer that is 50070024 that is divisible by both numbers.

Least Common Multiple (LCM) of 10006 and 10008 is 50070024.

LCM(10006,10008) = 50070024

LCM of 10006 and 10008

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

LCM of:
and

Least Common Multiple of 10006 and 10008

LCM of 10006 and 10008 is 50070024

Least common multiple can be found by multiplying the highest exponent prime factors of 10006 and 10008. First we will calculate the prime factors of 10006 and 10008.

Prime Factorization of 10006


2 10006
5003 5003
1

Prime factors of 10006 are 2,5003. Prime factorization of 10006 in exponential form is:

10006 = 21×50031

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 10006 and 10008.

LCM(10006,10008) = 23×32×1391×50031
LCM(10006,10008) = 50070024

Factors of 10006

List of positive integer factors of 10006 that divides 10006 without a remainder.

1, 2, 5003, 10006

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 10006 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 10006 and 10008, than apply into the LCM equation.

GCF(10006,10008) = 2
LCM(10006,10008) = ( 10006 × 10008) / 2
LCM(10006,10008) = 100140048 / 2
LCM(10006,10008) = 50070024

Properties of LCM 10006 and 10008

(i) The LCM of 10008 and 10006 is associative

LCM of 10006 and 10008 = LCM of 10008 and 10006

Related Least Common Multiples of 10006

Related Least Common Multiples of 10008

Frequently Asked Questions on LCM of 10006 and 10008

1. What is the LCM of 10006 and 10008?

Answer: LCM of 10006 and 10008 is 50070024.

2. What are the Factors of 10006?

Answer: Factors of 10006 are 1, 2, 5003, 10006. There are 4 integers that are factors of 10006. The greatest factor of 10006 is 10006.

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 10006 and 10008?

Answer:

Least Common Multiple of 10006 and 10008 = 50070024

Step 1: Find the prime factorization of 10006

10006 = 2 x 5003

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 = 50070024 = 2 x 2 x 2 x 3 x 3 x 139 x 5003

Step 4: Therefore, the least common multiple of 10006 and 10008 is 50070024.