Least Common Multiple of 8000 and 8006

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 8006 the smallest integer that is 32024000 that is divisible by both numbers.

Least Common Multiple (LCM) of 8000 and 8006 is 32024000.

LCM(8000,8006) = 32024000

LCM of 8000 and 8006

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

LCM of:
and

Least Common Multiple of 8000 and 8006

LCM of 8000 and 8006 is 32024000

Least common multiple can be found by multiplying the highest exponent prime factors of 8000 and 8006. First we will calculate the prime factors of 8000 and 8006.

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 8006


2 8006
4003 4003
1

Prime factors of 8006 are 2,4003. Prime factorization of 8006 in exponential form is:

8006 = 21×40031

Now multiplying the highest exponent prime factors to calculate the LCM of 8000 and 8006.

LCM(8000,8006) = 26×53×40031
LCM(8000,8006) = 32024000

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 8006

List of positive integer factors of 8006 that divides 8006 without a remainder.

1, 2, 4003, 8006

Least Common Multiple of 8000 and 8006 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 8006, than apply into the LCM equation.

GCF(8000,8006) = 2
LCM(8000,8006) = ( 8000 × 8006) / 2
LCM(8000,8006) = 64048000 / 2
LCM(8000,8006) = 32024000

Properties of LCM 8000 and 8006

(i) The LCM of 8006 and 8000 is associative

LCM of 8000 and 8006 = LCM of 8006 and 8000

Related Least Common Multiples of 8000

Related Least Common Multiples of 8006

Frequently Asked Questions on LCM of 8000 and 8006

1. What is the LCM of 8000 and 8006?

Answer: LCM of 8000 and 8006 is 32024000.

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 8006?

Answer: Factors of 8006 are 1, 2, 4003, 8006. There are 4 integers that are factors of 8006. The greatest factor of 8006 is 8006.

4. How to Find the LCM of 8000 and 8006?

Answer:

Least Common Multiple of 8000 and 8006 = 32024000

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 8006

8006 = 2 x 4003

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

LCM = 32024000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 4003

Step 4: Therefore, the least common multiple of 8000 and 8006 is 32024000.