Least Common Multiple of 2004 and 2005

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2004 and 2005 the smallest integer that is 4018020 that is divisible by both numbers.

Least Common Multiple (LCM) of 2004 and 2005 is 4018020.

LCM(2004,2005) = 4018020

LCM of 2004 and 2005

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

LCM of:
and

Least Common Multiple of 2004 and 2005

LCM of 2004 and 2005 is 4018020

Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2005. First we will calculate the prime factors of 2004 and 2005.

Prime Factorization of 2004


2 2004
2 1002
3 501
167 167
1

Prime factors of 2004 are 2, 3,167. Prime factorization of 2004 in exponential form is:

2004 = 22×31×1671

Prime Factorization of 2005


5 2005
401 401
1

Prime factors of 2005 are 5,401. Prime factorization of 2005 in exponential form is:

2005 = 51×4011

Now multiplying the highest exponent prime factors to calculate the LCM of 2004 and 2005.

LCM(2004,2005) = 22×31×51×1671×4011
LCM(2004,2005) = 4018020

Factors of 2004

List of positive integer factors of 2004 that divides 2004 without a remainder.

1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004

Factors of 2005

List of positive integer factors of 2005 that divides 2005 without a remainder.

1, 5, 401, 2005

Least Common Multiple of 2004 and 2005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2004 and 2005, than apply into the LCM equation.

GCF(2004,2005) = 1
LCM(2004,2005) = ( 2004 × 2005) / 1
LCM(2004,2005) = 4018020 / 1
LCM(2004,2005) = 4018020

Properties of LCM 2004 and 2005

(i) The LCM of 2005 and 2004 is associative

LCM of 2004 and 2005 = LCM of 2005 and 2004

Related Least Common Multiples of 2004

Related Least Common Multiples of 2005

Frequently Asked Questions on LCM of 2004 and 2005

1. What is the LCM of 2004 and 2005?

Answer: LCM of 2004 and 2005 is 4018020.

2. What are the Factors of 2004?

Answer: Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004. There are 12 integers that are factors of 2004. The greatest factor of 2004 is 2004.

3. What are the Factors of 2005?

Answer: Factors of 2005 are 1, 5, 401, 2005. There are 4 integers that are factors of 2005. The greatest factor of 2005 is 2005.

4. How to Find the LCM of 2004 and 2005?

Answer:

Least Common Multiple of 2004 and 2005 = 4018020

Step 1: Find the prime factorization of 2004

2004 = 2 x 2 x 3 x 167

Step 2: Find the prime factorization of 2005

2005 = 5 x 401

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

LCM = 4018020 = 2 x 2 x 3 x 5 x 167 x 401

Step 4: Therefore, the least common multiple of 2004 and 2005 is 4018020.