Least Common Multiple of 2004 and 2007

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 2007 the smallest integer that is 1340676 that is divisible by both numbers.

Least Common Multiple (LCM) of 2004 and 2007 is 1340676.

LCM(2004,2007) = 1340676

LCM of 2004 and 2007

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

LCM of:
and

Least Common Multiple of 2004 and 2007

LCM of 2004 and 2007 is 1340676

Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2007. First we will calculate the prime factors of 2004 and 2007.

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 2007


3 2007
3 669
223 223
1

Prime factors of 2007 are 3,223. Prime factorization of 2007 in exponential form is:

2007 = 32×2231

Now multiplying the highest exponent prime factors to calculate the LCM of 2004 and 2007.

LCM(2004,2007) = 22×32×1671×2231
LCM(2004,2007) = 1340676

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 2007

List of positive integer factors of 2007 that divides 2007 without a remainder.

1, 3, 9, 223, 669, 2007

Least Common Multiple of 2004 and 2007 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 2007, than apply into the LCM equation.

GCF(2004,2007) = 3
LCM(2004,2007) = ( 2004 × 2007) / 3
LCM(2004,2007) = 4022028 / 3
LCM(2004,2007) = 1340676

Properties of LCM 2004 and 2007

(i) The LCM of 2007 and 2004 is associative

LCM of 2004 and 2007 = LCM of 2007 and 2004

Related Least Common Multiples of 2004

Related Least Common Multiples of 2007

Frequently Asked Questions on LCM of 2004 and 2007

1. What is the LCM of 2004 and 2007?

Answer: LCM of 2004 and 2007 is 1340676.

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 2007?

Answer: Factors of 2007 are 1, 3, 9, 223, 669, 2007. There are 6 integers that are factors of 2007. The greatest factor of 2007 is 2007.

4. How to Find the LCM of 2004 and 2007?

Answer:

Least Common Multiple of 2004 and 2007 = 1340676

Step 1: Find the prime factorization of 2004

2004 = 2 x 2 x 3 x 167

Step 2: Find the prime factorization of 2007

2007 = 3 x 3 x 223

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

LCM = 1340676 = 2 x 2 x 3 x 3 x 167 x 223

Step 4: Therefore, the least common multiple of 2004 and 2007 is 1340676.