Least Common Multiple of 6000 and 6002

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 6002 the smallest integer that is 18006000 that is divisible by both numbers.

Least Common Multiple (LCM) of 6000 and 6002 is 18006000.

LCM(6000,6002) = 18006000

LCM of 6000 and 6002

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

LCM of:
and

Least Common Multiple of 6000 and 6002

LCM of 6000 and 6002 is 18006000

Least common multiple can be found by multiplying the highest exponent prime factors of 6000 and 6002. First we will calculate the prime factors of 6000 and 6002.

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 6002


2 6002
3001 3001
1

Prime factors of 6002 are 2,3001. Prime factorization of 6002 in exponential form is:

6002 = 21×30011

Now multiplying the highest exponent prime factors to calculate the LCM of 6000 and 6002.

LCM(6000,6002) = 24×31×53×30011
LCM(6000,6002) = 18006000

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 6002

List of positive integer factors of 6002 that divides 6002 without a remainder.

1, 2, 3001, 6002

Least Common Multiple of 6000 and 6002 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 6002, than apply into the LCM equation.

GCF(6000,6002) = 2
LCM(6000,6002) = ( 6000 × 6002) / 2
LCM(6000,6002) = 36012000 / 2
LCM(6000,6002) = 18006000

Properties of LCM 6000 and 6002

(i) The LCM of 6002 and 6000 is associative

LCM of 6000 and 6002 = LCM of 6002 and 6000

Related Least Common Multiples of 6000

Related Least Common Multiples of 6002

Frequently Asked Questions on LCM of 6000 and 6002

1. What is the LCM of 6000 and 6002?

Answer: LCM of 6000 and 6002 is 18006000.

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 6002?

Answer: Factors of 6002 are 1, 2, 3001, 6002. There are 4 integers that are factors of 6002. The greatest factor of 6002 is 6002.

4. How to Find the LCM of 6000 and 6002?

Answer:

Least Common Multiple of 6000 and 6002 = 18006000

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 6002

6002 = 2 x 3001

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

LCM = 18006000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 3001

Step 4: Therefore, the least common multiple of 6000 and 6002 is 18006000.