Least Common Multiple of 10000 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 10000 and 10008 the smallest integer that is 12510000 that is divisible by both numbers.

Least Common Multiple (LCM) of 10000 and 10008 is 12510000.

LCM(10000,10008) = 12510000

LCM of 10000 and 10008

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

LCM of:
and

Least Common Multiple of 10000 and 10008

LCM of 10000 and 10008 is 12510000

Least common multiple can be found by multiplying the highest exponent prime factors of 10000 and 10008. First we will calculate the prime factors of 10000 and 10008.

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 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 10000 and 10008.

LCM(10000,10008) = 24×32×54×1391
LCM(10000,10008) = 12510000

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 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 10000 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 10000 and 10008, than apply into the LCM equation.

GCF(10000,10008) = 8
LCM(10000,10008) = ( 10000 × 10008) / 8
LCM(10000,10008) = 100080000 / 8
LCM(10000,10008) = 12510000

Properties of LCM 10000 and 10008

(i) The LCM of 10008 and 10000 is associative

LCM of 10000 and 10008 = LCM of 10008 and 10000

Related Least Common Multiples of 10000

Related Least Common Multiples of 10008

Frequently Asked Questions on LCM of 10000 and 10008

1. What is the LCM of 10000 and 10008?

Answer: LCM of 10000 and 10008 is 12510000.

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 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 10000 and 10008?

Answer:

Least Common Multiple of 10000 and 10008 = 12510000

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 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 = 12510000 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 5 x 139

Step 4: Therefore, the least common multiple of 10000 and 10008 is 12510000.