Least Common Multiple of 6000 and 6004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6000 and 6004 the smallest integer that is 9006000 that is divisible by both numbers.

Least Common Multiple (LCM) of 6000 and 6004 is 9006000.

LCM(6000,6004) = 9006000

LCM of 6000 and 6004

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

LCM of:
and

Least Common Multiple of 6000 and 6004

LCM of 6000 and 6004 is 9006000

Least common multiple can be found by multiplying the highest exponent prime factors of 6000 and 6004. First we will calculate the prime factors of 6000 and 6004.

Prime Factorization of 6000


2 6000
2 3000
2 1500
2 750
3 375
5 125
5 25
5 5
1

Prime factors of 6000 are 2, 3,5. Prime factorization of 6000 in exponential form is:

6000 = 24×31×53

Prime Factorization of 6004


2 6004
2 3002
19 1501
79 79
1

Prime factors of 6004 are 2, 19,79. Prime factorization of 6004 in exponential form is:

6004 = 22×191×791

Now multiplying the highest exponent prime factors to calculate the LCM of 6000 and 6004.

LCM(6000,6004) = 24×31×53×191×791
LCM(6000,6004) = 9006000

Factors of 6000

List of positive integer factors of 6000 that divides 6000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000

Factors of 6004

List of positive integer factors of 6004 that divides 6004 without a remainder.

1, 2, 4, 19, 38, 76, 79, 158, 316, 1501, 3002, 6004

Least Common Multiple of 6000 and 6004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6000 and 6004, than apply into the LCM equation.

GCF(6000,6004) = 4
LCM(6000,6004) = ( 6000 × 6004) / 4
LCM(6000,6004) = 36024000 / 4
LCM(6000,6004) = 9006000

Properties of LCM 6000 and 6004

(i) The LCM of 6004 and 6000 is associative

LCM of 6000 and 6004 = LCM of 6004 and 6000

Related Least Common Multiples of 6000

Related Least Common Multiples of 6004

Frequently Asked Questions on LCM of 6000 and 6004

1. What is the LCM of 6000 and 6004?

Answer: LCM of 6000 and 6004 is 9006000.

2. What are the Factors of 6000?

Answer: Factors of 6000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000. There are 40 integers that are factors of 6000. The greatest factor of 6000 is 6000.

3. What are the Factors of 6004?

Answer: Factors of 6004 are 1, 2, 4, 19, 38, 76, 79, 158, 316, 1501, 3002, 6004. There are 12 integers that are factors of 6004. The greatest factor of 6004 is 6004.

4. How to Find the LCM of 6000 and 6004?

Answer:

Least Common Multiple of 6000 and 6004 = 9006000

Step 1: Find the prime factorization of 6000

6000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 6004

6004 = 2 x 2 x 19 x 79

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

LCM = 9006000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 19 x 79

Step 4: Therefore, the least common multiple of 6000 and 6004 is 9006000.