Least Common Multiple of 2005 and 2006

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2005 and 2006 the smallest integer that is 4022030 that is divisible by both numbers.

Least Common Multiple (LCM) of 2005 and 2006 is 4022030.

LCM(2005,2006) = 4022030

LCM of 2005 and 2006

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

LCM of:
and

Least Common Multiple of 2005 and 2006

LCM of 2005 and 2006 is 4022030

Least common multiple can be found by multiplying the highest exponent prime factors of 2005 and 2006. First we will calculate the prime factors of 2005 and 2006.

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

Prime Factorization of 2006


2 2006
17 1003
59 59
1

Prime factors of 2006 are 2, 17,59. Prime factorization of 2006 in exponential form is:

2006 = 21×171×591

Now multiplying the highest exponent prime factors to calculate the LCM of 2005 and 2006.

LCM(2005,2006) = 21×51×171×591×4011
LCM(2005,2006) = 4022030

Factors of 2005

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

1, 5, 401, 2005

Factors of 2006

List of positive integer factors of 2006 that divides 2006 without a remainder.

1, 2, 17, 34, 59, 118, 1003, 2006

Least Common Multiple of 2005 and 2006 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2005 and 2006, than apply into the LCM equation.

GCF(2005,2006) = 1
LCM(2005,2006) = ( 2005 × 2006) / 1
LCM(2005,2006) = 4022030 / 1
LCM(2005,2006) = 4022030

Properties of LCM 2005 and 2006

(i) The LCM of 2006 and 2005 is associative

LCM of 2005 and 2006 = LCM of 2006 and 2005

Related Least Common Multiples of 2005

Related Least Common Multiples of 2006

Frequently Asked Questions on LCM of 2005 and 2006

1. What is the LCM of 2005 and 2006?

Answer: LCM of 2005 and 2006 is 4022030.

2. 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.

3. What are the Factors of 2006?

Answer: Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. There are 8 integers that are factors of 2006. The greatest factor of 2006 is 2006.

4. How to Find the LCM of 2005 and 2006?

Answer:

Least Common Multiple of 2005 and 2006 = 4022030

Step 1: Find the prime factorization of 2005

2005 = 5 x 401

Step 2: Find the prime factorization of 2006

2006 = 2 x 17 x 59

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

LCM = 4022030 = 2 x 5 x 17 x 59 x 401

Step 4: Therefore, the least common multiple of 2005 and 2006 is 4022030.