Least Common Multiple of 3003 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 3003 and 3004 the smallest integer that is 9021012 that is divisible by both numbers.

Least Common Multiple (LCM) of 3003 and 3004 is 9021012.

LCM(3003,3004) = 9021012

LCM of 3003 and 3004

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

LCM of:
and

Least Common Multiple of 3003 and 3004

LCM of 3003 and 3004 is 9021012

Least common multiple can be found by multiplying the highest exponent prime factors of 3003 and 3004. First we will calculate the prime factors of 3003 and 3004.

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

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 3003 and 3004.

LCM(3003,3004) = 22×31×71×111×131×7511
LCM(3003,3004) = 9021012

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

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 3003 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 3003 and 3004, than apply into the LCM equation.

GCF(3003,3004) = 1
LCM(3003,3004) = ( 3003 × 3004) / 1
LCM(3003,3004) = 9021012 / 1
LCM(3003,3004) = 9021012

Properties of LCM 3003 and 3004

(i) The LCM of 3004 and 3003 is associative

LCM of 3003 and 3004 = LCM of 3004 and 3003

Related Least Common Multiples of 3003

Related Least Common Multiples of 3004

Frequently Asked Questions on LCM of 3003 and 3004

1. What is the LCM of 3003 and 3004?

Answer: LCM of 3003 and 3004 is 9021012.

2. 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.

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 3003 and 3004?

Answer:

Least Common Multiple of 3003 and 3004 = 9021012

Step 1: Find the prime factorization of 3003

3003 = 3 x 7 x 11 x 13

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 = 9021012 = 2 x 2 x 3 x 7 x 11 x 13 x 751

Step 4: Therefore, the least common multiple of 3003 and 3004 is 9021012.