Least Common Multiple of 8000 and 8005

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8000 and 8005 the smallest integer that is 12808000 that is divisible by both numbers.

Least Common Multiple (LCM) of 8000 and 8005 is 12808000.

LCM(8000,8005) = 12808000

LCM of 8000 and 8005

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

LCM of:
and

Least Common Multiple of 8000 and 8005

LCM of 8000 and 8005 is 12808000

Least common multiple can be found by multiplying the highest exponent prime factors of 8000 and 8005. First we will calculate the prime factors of 8000 and 8005.

Prime Factorization of 8000


2 8000
2 4000
2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 8000 are 2,5. Prime factorization of 8000 in exponential form is:

8000 = 26×53

Prime Factorization of 8005


5 8005
1601 1601
1

Prime factors of 8005 are 5,1601. Prime factorization of 8005 in exponential form is:

8005 = 51×16011

Now multiplying the highest exponent prime factors to calculate the LCM of 8000 and 8005.

LCM(8000,8005) = 26×53×16011
LCM(8000,8005) = 12808000

Factors of 8000

List of positive integer factors of 8000 that divides 8000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000

Factors of 8005

List of positive integer factors of 8005 that divides 8005 without a remainder.

1, 5, 1601, 8005

Least Common Multiple of 8000 and 8005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8000 and 8005, than apply into the LCM equation.

GCF(8000,8005) = 5
LCM(8000,8005) = ( 8000 × 8005) / 5
LCM(8000,8005) = 64040000 / 5
LCM(8000,8005) = 12808000

Properties of LCM 8000 and 8005

(i) The LCM of 8005 and 8000 is associative

LCM of 8000 and 8005 = LCM of 8005 and 8000

Related Least Common Multiples of 8000

Related Least Common Multiples of 8005

Frequently Asked Questions on LCM of 8000 and 8005

1. What is the LCM of 8000 and 8005?

Answer: LCM of 8000 and 8005 is 12808000.

2. What are the Factors of 8000?

Answer: Factors of 8000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000. There are 28 integers that are factors of 8000. The greatest factor of 8000 is 8000.

3. What are the Factors of 8005?

Answer: Factors of 8005 are 1, 5, 1601, 8005. There are 4 integers that are factors of 8005. The greatest factor of 8005 is 8005.

4. How to Find the LCM of 8000 and 8005?

Answer:

Least Common Multiple of 8000 and 8005 = 12808000

Step 1: Find the prime factorization of 8000

8000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 8005

8005 = 5 x 1601

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

LCM = 12808000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 1601

Step 4: Therefore, the least common multiple of 8000 and 8005 is 12808000.