Least Common Multiple of 3000 and 3006

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 3006 the smallest integer that is 1503000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3006 is 1503000.

LCM(3000,3006) = 1503000

LCM of 3000 and 3006

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

LCM of:
and

Least Common Multiple of 3000 and 3006

LCM of 3000 and 3006 is 1503000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3006. First we will calculate the prime factors of 3000 and 3006.

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 3006


2 3006
3 1503
3 501
167 167
1

Prime factors of 3006 are 2, 3,167. Prime factorization of 3006 in exponential form is:

3006 = 21×32×1671

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3006.

LCM(3000,3006) = 23×32×53×1671
LCM(3000,3006) = 1503000

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 3006

List of positive integer factors of 3006 that divides 3006 without a remainder.

1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006

Least Common Multiple of 3000 and 3006 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 3006, than apply into the LCM equation.

GCF(3000,3006) = 6
LCM(3000,3006) = ( 3000 × 3006) / 6
LCM(3000,3006) = 9018000 / 6
LCM(3000,3006) = 1503000

Properties of LCM 3000 and 3006

(i) The LCM of 3006 and 3000 is associative

LCM of 3000 and 3006 = LCM of 3006 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3006

Frequently Asked Questions on LCM of 3000 and 3006

1. What is the LCM of 3000 and 3006?

Answer: LCM of 3000 and 3006 is 1503000.

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 3006?

Answer: Factors of 3006 are 1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006. There are 12 integers that are factors of 3006. The greatest factor of 3006 is 3006.

4. How to Find the LCM of 3000 and 3006?

Answer:

Least Common Multiple of 3000 and 3006 = 1503000

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 3006

3006 = 2 x 3 x 3 x 167

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

LCM = 1503000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 167

Step 4: Therefore, the least common multiple of 3000 and 3006 is 1503000.