Least Common Multiple of 3003 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 3003 and 3006 the smallest integer that is 3009006 that is divisible by both numbers.

Least Common Multiple (LCM) of 3003 and 3006 is 3009006.

LCM(3003,3006) = 3009006

LCM of 3003 and 3006

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

LCM of:
and

Least Common Multiple of 3003 and 3006

LCM of 3003 and 3006 is 3009006

Least common multiple can be found by multiplying the highest exponent prime factors of 3003 and 3006. First we will calculate the prime factors of 3003 and 3006.

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 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 3003 and 3006.

LCM(3003,3006) = 21×32×71×111×131×1671
LCM(3003,3006) = 3009006

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 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 3003 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 3003 and 3006, than apply into the LCM equation.

GCF(3003,3006) = 3
LCM(3003,3006) = ( 3003 × 3006) / 3
LCM(3003,3006) = 9027018 / 3
LCM(3003,3006) = 3009006

Properties of LCM 3003 and 3006

(i) The LCM of 3006 and 3003 is associative

LCM of 3003 and 3006 = LCM of 3006 and 3003

Related Least Common Multiples of 3003

Related Least Common Multiples of 3006

Frequently Asked Questions on LCM of 3003 and 3006

1. What is the LCM of 3003 and 3006?

Answer: LCM of 3003 and 3006 is 3009006.

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 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 3003 and 3006?

Answer:

Least Common Multiple of 3003 and 3006 = 3009006

Step 1: Find the prime factorization of 3003

3003 = 3 x 7 x 11 x 13

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 = 3009006 = 2 x 3 x 3 x 7 x 11 x 13 x 167

Step 4: Therefore, the least common multiple of 3003 and 3006 is 3009006.