Least Common Multiple of 3000 and 3005

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 3005 the smallest integer that is 1803000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3005 is 1803000.

LCM(3000,3005) = 1803000

LCM of 3000 and 3005

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

LCM of:
and

Least Common Multiple of 3000 and 3005

LCM of 3000 and 3005 is 1803000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3005. First we will calculate the prime factors of 3000 and 3005.

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 3005


5 3005
601 601
1

Prime factors of 3005 are 5,601. Prime factorization of 3005 in exponential form is:

3005 = 51×6011

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3005.

LCM(3000,3005) = 23×31×53×6011
LCM(3000,3005) = 1803000

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 3005

List of positive integer factors of 3005 that divides 3005 without a remainder.

1, 5, 601, 3005

Least Common Multiple of 3000 and 3005 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 3005, than apply into the LCM equation.

GCF(3000,3005) = 5
LCM(3000,3005) = ( 3000 × 3005) / 5
LCM(3000,3005) = 9015000 / 5
LCM(3000,3005) = 1803000

Properties of LCM 3000 and 3005

(i) The LCM of 3005 and 3000 is associative

LCM of 3000 and 3005 = LCM of 3005 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3005

Frequently Asked Questions on LCM of 3000 and 3005

1. What is the LCM of 3000 and 3005?

Answer: LCM of 3000 and 3005 is 1803000.

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 3005?

Answer: Factors of 3005 are 1, 5, 601, 3005. There are 4 integers that are factors of 3005. The greatest factor of 3005 is 3005.

4. How to Find the LCM of 3000 and 3005?

Answer:

Least Common Multiple of 3000 and 3005 = 1803000

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 3005

3005 = 5 x 601

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

LCM = 1803000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 601

Step 4: Therefore, the least common multiple of 3000 and 3005 is 1803000.