Least Common Multiple of 8000 and 8004

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 8004 the smallest integer that is 16008000 that is divisible by both numbers.

Least Common Multiple (LCM) of 8000 and 8004 is 16008000.

LCM(8000,8004) = 16008000

LCM of 8000 and 8004

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

LCM of:
and

Least Common Multiple of 8000 and 8004

LCM of 8000 and 8004 is 16008000

Least common multiple can be found by multiplying the highest exponent prime factors of 8000 and 8004. First we will calculate the prime factors of 8000 and 8004.

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 8004


2 8004
2 4002
3 2001
23 667
29 29
1

Prime factors of 8004 are 2, 3, 23,29. Prime factorization of 8004 in exponential form is:

8004 = 22×31×231×291

Now multiplying the highest exponent prime factors to calculate the LCM of 8000 and 8004.

LCM(8000,8004) = 26×31×53×231×291
LCM(8000,8004) = 16008000

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 8004

List of positive integer factors of 8004 that divides 8004 without a remainder.

1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004

Least Common Multiple of 8000 and 8004 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 8004, than apply into the LCM equation.

GCF(8000,8004) = 4
LCM(8000,8004) = ( 8000 × 8004) / 4
LCM(8000,8004) = 64032000 / 4
LCM(8000,8004) = 16008000

Properties of LCM 8000 and 8004

(i) The LCM of 8004 and 8000 is associative

LCM of 8000 and 8004 = LCM of 8004 and 8000

Related Least Common Multiples of 8000

Related Least Common Multiples of 8004

Frequently Asked Questions on LCM of 8000 and 8004

1. What is the LCM of 8000 and 8004?

Answer: LCM of 8000 and 8004 is 16008000.

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 8004?

Answer: Factors of 8004 are 1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004. There are 24 integers that are factors of 8004. The greatest factor of 8004 is 8004.

4. How to Find the LCM of 8000 and 8004?

Answer:

Least Common Multiple of 8000 and 8004 = 16008000

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 8004

8004 = 2 x 2 x 3 x 23 x 29

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

LCM = 16008000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 23 x 29

Step 4: Therefore, the least common multiple of 8000 and 8004 is 16008000.