Least Common Multiple of 3000 and 3004

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 3004 the smallest integer that is 2253000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3004 is 2253000.

LCM(3000,3004) = 2253000

LCM of 3000 and 3004

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

LCM of:
and

Least Common Multiple of 3000 and 3004

LCM of 3000 and 3004 is 2253000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3004. First we will calculate the prime factors of 3000 and 3004.

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 3004


2 3004
2 1502
751 751
1

Prime factors of 3004 are 2,751. Prime factorization of 3004 in exponential form is:

3004 = 22×7511

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3004.

LCM(3000,3004) = 23×31×53×7511
LCM(3000,3004) = 2253000

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 3004

List of positive integer factors of 3004 that divides 3004 without a remainder.

1, 2, 4, 751, 1502, 3004

Least Common Multiple of 3000 and 3004 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 3004, than apply into the LCM equation.

GCF(3000,3004) = 4
LCM(3000,3004) = ( 3000 × 3004) / 4
LCM(3000,3004) = 9012000 / 4
LCM(3000,3004) = 2253000

Properties of LCM 3000 and 3004

(i) The LCM of 3004 and 3000 is associative

LCM of 3000 and 3004 = LCM of 3004 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3004

Frequently Asked Questions on LCM of 3000 and 3004

1. What is the LCM of 3000 and 3004?

Answer: LCM of 3000 and 3004 is 2253000.

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 3004?

Answer: Factors of 3004 are 1, 2, 4, 751, 1502, 3004. There are 6 integers that are factors of 3004. The greatest factor of 3004 is 3004.

4. How to Find the LCM of 3000 and 3004?

Answer:

Least Common Multiple of 3000 and 3004 = 2253000

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 3004

3004 = 2 x 2 x 751

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

LCM = 2253000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 751

Step 4: Therefore, the least common multiple of 3000 and 3004 is 2253000.