Least Common Multiple of 3000 and 3007

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 3007 the smallest integer that is 9021000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3007 is 9021000.

LCM(3000,3007) = 9021000

LCM of 3000 and 3007

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

LCM of:
and

Least Common Multiple of 3000 and 3007

LCM of 3000 and 3007 is 9021000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3007. First we will calculate the prime factors of 3000 and 3007.

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 3007


31 3007
97 97
1

Prime factors of 3007 are 31,97. Prime factorization of 3007 in exponential form is:

3007 = 311×971

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3007.

LCM(3000,3007) = 23×31×53×311×971
LCM(3000,3007) = 9021000

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 3007

List of positive integer factors of 3007 that divides 3007 without a remainder.

1, 31, 97, 3007

Least Common Multiple of 3000 and 3007 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 3007, than apply into the LCM equation.

GCF(3000,3007) = 1
LCM(3000,3007) = ( 3000 × 3007) / 1
LCM(3000,3007) = 9021000 / 1
LCM(3000,3007) = 9021000

Properties of LCM 3000 and 3007

(i) The LCM of 3007 and 3000 is associative

LCM of 3000 and 3007 = LCM of 3007 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3007

Frequently Asked Questions on LCM of 3000 and 3007

1. What is the LCM of 3000 and 3007?

Answer: LCM of 3000 and 3007 is 9021000.

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 3007?

Answer: Factors of 3007 are 1, 31, 97, 3007. There are 4 integers that are factors of 3007. The greatest factor of 3007 is 3007.

4. How to Find the LCM of 3000 and 3007?

Answer:

Least Common Multiple of 3000 and 3007 = 9021000

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 3007

3007 = 31 x 97

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

LCM = 9021000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 31 x 97

Step 4: Therefore, the least common multiple of 3000 and 3007 is 9021000.