Least Common Multiple of 2004 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 2004 and 2006 the smallest integer that is 2010012 that is divisible by both numbers.

Least Common Multiple (LCM) of 2004 and 2006 is 2010012.

LCM(2004,2006) = 2010012

LCM of 2004 and 2006

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

LCM of:
and

Least Common Multiple of 2004 and 2006

LCM of 2004 and 2006 is 2010012

Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2006. First we will calculate the prime factors of 2004 and 2006.

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 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 2004 and 2006.

LCM(2004,2006) = 22×31×171×591×1671
LCM(2004,2006) = 2010012

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 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 2004 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 2004 and 2006, than apply into the LCM equation.

GCF(2004,2006) = 2
LCM(2004,2006) = ( 2004 × 2006) / 2
LCM(2004,2006) = 4020024 / 2
LCM(2004,2006) = 2010012

Properties of LCM 2004 and 2006

(i) The LCM of 2006 and 2004 is associative

LCM of 2004 and 2006 = LCM of 2006 and 2004

Related Least Common Multiples of 2004

Related Least Common Multiples of 2006

Frequently Asked Questions on LCM of 2004 and 2006

1. What is the LCM of 2004 and 2006?

Answer: LCM of 2004 and 2006 is 2010012.

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 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 2004 and 2006?

Answer:

Least Common Multiple of 2004 and 2006 = 2010012

Step 1: Find the prime factorization of 2004

2004 = 2 x 2 x 3 x 167

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 = 2010012 = 2 x 2 x 3 x 17 x 59 x 167

Step 4: Therefore, the least common multiple of 2004 and 2006 is 2010012.