Least Common Multiple of 3000 and 3001

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3000 and 3001 the smallest integer that is 9003000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3001 is 9003000.

LCM(3000,3001) = 9003000

LCM of 3000 and 3001

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

LCM of:
and

Least Common Multiple of 3000 and 3001

LCM of 3000 and 3001 is 9003000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3001. First we will calculate the prime factors of 3000 and 3001.

Prime Factorization of 3000


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

Prime factors of 3000 are 2, 3,5. Prime factorization of 3000 in exponential form is:

3000 = 23×31×53

Prime Factorization of 3001


3001 3001
1

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

3001 = 30011

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3001.

LCM(3000,3001) = 23×31×53×30011
LCM(3000,3001) = 9003000

Factors of 3000

List of positive integer factors of 3000 that divides 3000 without a remainder.

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

Factors of 3001

List of positive integer factors of 3001 that divides 3001 without a remainder.

1, 3001

Least Common Multiple of 3000 and 3001 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3000 and 3001, than apply into the LCM equation.

GCF(3000,3001) = 1
LCM(3000,3001) = ( 3000 × 3001) / 1
LCM(3000,3001) = 9003000 / 1
LCM(3000,3001) = 9003000

Properties of LCM 3000 and 3001

(i) The LCM of 3001 and 3000 is associative

LCM of 3000 and 3001 = LCM of 3001 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3001

Frequently Asked Questions on LCM of 3000 and 3001

1. What is the LCM of 3000 and 3001?

Answer: LCM of 3000 and 3001 is 9003000.

2. What are the Factors of 3000?

Answer: Factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000. There are 32 integers that are factors of 3000. The greatest factor of 3000 is 3000.

3. What are the Factors of 3001?

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

4. How to Find the LCM of 3000 and 3001?

Answer:

Least Common Multiple of 3000 and 3001 = 9003000

Step 1: Find the prime factorization of 3000

3000 = 2 x 2 x 2 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 3001

3001 = 3001

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

LCM = 9003000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 3001

Step 4: Therefore, the least common multiple of 3000 and 3001 is 9003000.