Least Common Multiple of 10006 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 10006 and 10010 the smallest integer that is 50080030 that is divisible by both numbers.

Least Common Multiple (LCM) of 10006 and 10010 is 50080030.

LCM(10006,10010) = 50080030

LCM of 10006 and 10010

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

LCM of:
and

Least Common Multiple of 10006 and 10010

LCM of 10006 and 10010 is 50080030

Least common multiple can be found by multiplying the highest exponent prime factors of 10006 and 10010. First we will calculate the prime factors of 10006 and 10010.

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 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 10006 and 10010.

LCM(10006,10010) = 21×51×71×111×131×50031
LCM(10006,10010) = 50080030

Factors of 10006

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

1, 2, 5003, 10006

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 10006 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 10006 and 10010, than apply into the LCM equation.

GCF(10006,10010) = 2
LCM(10006,10010) = ( 10006 × 10010) / 2
LCM(10006,10010) = 100160060 / 2
LCM(10006,10010) = 50080030

Properties of LCM 10006 and 10010

(i) The LCM of 10010 and 10006 is associative

LCM of 10006 and 10010 = LCM of 10010 and 10006

Related Least Common Multiples of 10006

Related Least Common Multiples of 10010

Frequently Asked Questions on LCM of 10006 and 10010

1. What is the LCM of 10006 and 10010?

Answer: LCM of 10006 and 10010 is 50080030.

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 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 10006 and 10010?

Answer:

Least Common Multiple of 10006 and 10010 = 50080030

Step 1: Find the prime factorization of 10006

10006 = 2 x 5003

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 = 50080030 = 2 x 5 x 7 x 11 x 13 x 5003

Step 4: Therefore, the least common multiple of 10006 and 10010 is 50080030.