Least Common Multiple of 3000 and 3003

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 3003 the smallest integer that is 3003000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3003 is 3003000.

LCM(3000,3003) = 3003000

LCM of 3000 and 3003

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

LCM of:
and

Least Common Multiple of 3000 and 3003

LCM of 3000 and 3003 is 3003000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3003. First we will calculate the prime factors of 3000 and 3003.

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 3003


3 3003
7 1001
11 143
13 13
1

Prime factors of 3003 are 3, 7, 11,13. Prime factorization of 3003 in exponential form is:

3003 = 31×71×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3003.

LCM(3000,3003) = 23×31×53×71×111×131
LCM(3000,3003) = 3003000

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 3003

List of positive integer factors of 3003 that divides 3003 without a remainder.

1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003

Least Common Multiple of 3000 and 3003 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 3003, than apply into the LCM equation.

GCF(3000,3003) = 3
LCM(3000,3003) = ( 3000 × 3003) / 3
LCM(3000,3003) = 9009000 / 3
LCM(3000,3003) = 3003000

Properties of LCM 3000 and 3003

(i) The LCM of 3003 and 3000 is associative

LCM of 3000 and 3003 = LCM of 3003 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3003

Frequently Asked Questions on LCM of 3000 and 3003

1. What is the LCM of 3000 and 3003?

Answer: LCM of 3000 and 3003 is 3003000.

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 3003?

Answer: Factors of 3003 are 1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003. There are 16 integers that are factors of 3003. The greatest factor of 3003 is 3003.

4. How to Find the LCM of 3000 and 3003?

Answer:

Least Common Multiple of 3000 and 3003 = 3003000

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 3003

3003 = 3 x 7 x 11 x 13

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

LCM = 3003000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7 x 11 x 13

Step 4: Therefore, the least common multiple of 3000 and 3003 is 3003000.