Least Common Multiple of 10000 and 10007

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10000 and 10007 the smallest integer that is 100070000 that is divisible by both numbers.

Least Common Multiple (LCM) of 10000 and 10007 is 100070000.

LCM(10000,10007) = 100070000

LCM of 10000 and 10007

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

LCM of:
and

Least Common Multiple of 10000 and 10007

LCM of 10000 and 10007 is 100070000

Least common multiple can be found by multiplying the highest exponent prime factors of 10000 and 10007. First we will calculate the prime factors of 10000 and 10007.

Prime Factorization of 10000


2 10000
2 5000
2 2500
2 1250
5 625
5 125
5 25
5 5
1

Prime factors of 10000 are 2,5. Prime factorization of 10000 in exponential form is:

10000 = 24×54

Prime Factorization of 10007


10007 10007
1

Prime factors of 10007 are 10007. Prime factorization of 10007 in exponential form is:

10007 = 100071

Now multiplying the highest exponent prime factors to calculate the LCM of 10000 and 10007.

LCM(10000,10007) = 24×54×100071
LCM(10000,10007) = 100070000

Factors of 10000

List of positive integer factors of 10000 that divides 10000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000

Factors of 10007

List of positive integer factors of 10007 that divides 10007 without a remainder.

1, 10007

Least Common Multiple of 10000 and 10007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10000 and 10007, than apply into the LCM equation.

GCF(10000,10007) = 1
LCM(10000,10007) = ( 10000 × 10007) / 1
LCM(10000,10007) = 100070000 / 1
LCM(10000,10007) = 100070000

Properties of LCM 10000 and 10007

(i) The LCM of 10007 and 10000 is associative

LCM of 10000 and 10007 = LCM of 10007 and 10000

Related Least Common Multiples of 10000

Related Least Common Multiples of 10007

Frequently Asked Questions on LCM of 10000 and 10007

1. What is the LCM of 10000 and 10007?

Answer: LCM of 10000 and 10007 is 100070000.

2. What are the Factors of 10000?

Answer: Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000. There are 25 integers that are factors of 10000. The greatest factor of 10000 is 10000.

3. What are the Factors of 10007?

Answer: Factors of 10007 are 1, 10007. There are 2 integers that are factors of 10007. The greatest factor of 10007 is 10007.

4. How to Find the LCM of 10000 and 10007?

Answer:

Least Common Multiple of 10000 and 10007 = 100070000

Step 1: Find the prime factorization of 10000

10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5

Step 2: Find the prime factorization of 10007

10007 = 10007

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

LCM = 100070000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 10007

Step 4: Therefore, the least common multiple of 10000 and 10007 is 100070000.