Least Common Multiple of 2004 and 2008

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 2008 the smallest integer that is 1006008 that is divisible by both numbers.

Least Common Multiple (LCM) of 2004 and 2008 is 1006008.

LCM(2004,2008) = 1006008

LCM of 2004 and 2008

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

LCM of:
and

Least Common Multiple of 2004 and 2008

LCM of 2004 and 2008 is 1006008

Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2008. First we will calculate the prime factors of 2004 and 2008.

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 2008


2 2008
2 1004
2 502
251 251
1

Prime factors of 2008 are 2,251. Prime factorization of 2008 in exponential form is:

2008 = 23×2511

Now multiplying the highest exponent prime factors to calculate the LCM of 2004 and 2008.

LCM(2004,2008) = 23×31×1671×2511
LCM(2004,2008) = 1006008

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 2008

List of positive integer factors of 2008 that divides 2008 without a remainder.

1, 2, 4, 8, 251, 502, 1004, 2008

Least Common Multiple of 2004 and 2008 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 2008, than apply into the LCM equation.

GCF(2004,2008) = 4
LCM(2004,2008) = ( 2004 × 2008) / 4
LCM(2004,2008) = 4024032 / 4
LCM(2004,2008) = 1006008

Properties of LCM 2004 and 2008

(i) The LCM of 2008 and 2004 is associative

LCM of 2004 and 2008 = LCM of 2008 and 2004

Related Least Common Multiples of 2004

Related Least Common Multiples of 2008

Frequently Asked Questions on LCM of 2004 and 2008

1. What is the LCM of 2004 and 2008?

Answer: LCM of 2004 and 2008 is 1006008.

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 2008?

Answer: Factors of 2008 are 1, 2, 4, 8, 251, 502, 1004, 2008. There are 8 integers that are factors of 2008. The greatest factor of 2008 is 2008.

4. How to Find the LCM of 2004 and 2008?

Answer:

Least Common Multiple of 2004 and 2008 = 1006008

Step 1: Find the prime factorization of 2004

2004 = 2 x 2 x 3 x 167

Step 2: Find the prime factorization of 2008

2008 = 2 x 2 x 2 x 251

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

LCM = 1006008 = 2 x 2 x 2 x 3 x 167 x 251

Step 4: Therefore, the least common multiple of 2004 and 2008 is 1006008.