Least Common Multiple of 2003 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 2003 and 2005 the smallest integer that is 4016015 that is divisible by both numbers.

Least Common Multiple (LCM) of 2003 and 2005 is 4016015.

LCM(2003,2005) = 4016015

LCM of 2003 and 2005

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

LCM of:
and

Least Common Multiple of 2003 and 2005

LCM of 2003 and 2005 is 4016015

Least common multiple can be found by multiplying the highest exponent prime factors of 2003 and 2005. First we will calculate the prime factors of 2003 and 2005.

Prime Factorization of 2003


2003 2003
1

Prime factors of 2003 are 2003. Prime factorization of 2003 in exponential form is:

2003 = 20031

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 2003 and 2005.

LCM(2003,2005) = 51×4011×20031
LCM(2003,2005) = 4016015

Factors of 2003

List of positive integer factors of 2003 that divides 2003 without a remainder.

1, 2003

Factors of 2005

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

1, 5, 401, 2005

Least Common Multiple of 2003 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 2003 and 2005, than apply into the LCM equation.

GCF(2003,2005) = 1
LCM(2003,2005) = ( 2003 × 2005) / 1
LCM(2003,2005) = 4016015 / 1
LCM(2003,2005) = 4016015

Properties of LCM 2003 and 2005

(i) The LCM of 2005 and 2003 is associative

LCM of 2003 and 2005 = LCM of 2005 and 2003

Related Least Common Multiples of 2003

Related Least Common Multiples of 2005

Frequently Asked Questions on LCM of 2003 and 2005

1. What is the LCM of 2003 and 2005?

Answer: LCM of 2003 and 2005 is 4016015.

2. What are the Factors of 2003?

Answer: Factors of 2003 are 1, 2003. There are 2 integers that are factors of 2003. The greatest factor of 2003 is 2003.

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 2003 and 2005?

Answer:

Least Common Multiple of 2003 and 2005 = 4016015

Step 1: Find the prime factorization of 2003

2003 = 2003

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 = 4016015 = 5 x 401 x 2003

Step 4: Therefore, the least common multiple of 2003 and 2005 is 4016015.