Least Common Multiple of 6000 and 6005

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 6005 the smallest integer that is 7206000 that is divisible by both numbers.

Least Common Multiple (LCM) of 6000 and 6005 is 7206000.

LCM(6000,6005) = 7206000

LCM of 6000 and 6005

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

LCM of:
and

Least Common Multiple of 6000 and 6005

LCM of 6000 and 6005 is 7206000

Least common multiple can be found by multiplying the highest exponent prime factors of 6000 and 6005. First we will calculate the prime factors of 6000 and 6005.

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 6005


5 6005
1201 1201
1

Prime factors of 6005 are 5,1201. Prime factorization of 6005 in exponential form is:

6005 = 51×12011

Now multiplying the highest exponent prime factors to calculate the LCM of 6000 and 6005.

LCM(6000,6005) = 24×31×53×12011
LCM(6000,6005) = 7206000

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 6005

List of positive integer factors of 6005 that divides 6005 without a remainder.

1, 5, 1201, 6005

Least Common Multiple of 6000 and 6005 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 6005, than apply into the LCM equation.

GCF(6000,6005) = 5
LCM(6000,6005) = ( 6000 × 6005) / 5
LCM(6000,6005) = 36030000 / 5
LCM(6000,6005) = 7206000

Properties of LCM 6000 and 6005

(i) The LCM of 6005 and 6000 is associative

LCM of 6000 and 6005 = LCM of 6005 and 6000

Related Least Common Multiples of 6000

Related Least Common Multiples of 6005

Frequently Asked Questions on LCM of 6000 and 6005

1. What is the LCM of 6000 and 6005?

Answer: LCM of 6000 and 6005 is 7206000.

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 6005?

Answer: Factors of 6005 are 1, 5, 1201, 6005. There are 4 integers that are factors of 6005. The greatest factor of 6005 is 6005.

4. How to Find the LCM of 6000 and 6005?

Answer:

Least Common Multiple of 6000 and 6005 = 7206000

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 6005

6005 = 5 x 1201

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

LCM = 7206000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 1201

Step 4: Therefore, the least common multiple of 6000 and 6005 is 7206000.