Least Common Multiple of 2000 and 2004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2000 and 2004 the smallest integer that is 1002000 that is divisible by both numbers.

Least Common Multiple (LCM) of 2000 and 2004 is 1002000.

LCM(2000,2004) = 1002000

LCM of 2000 and 2004

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

LCM of:
and

Least Common Multiple of 2000 and 2004

LCM of 2000 and 2004 is 1002000

Least common multiple can be found by multiplying the highest exponent prime factors of 2000 and 2004. First we will calculate the prime factors of 2000 and 2004.

Prime Factorization of 2000


2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 2000 are 2,5. Prime factorization of 2000 in exponential form is:

2000 = 24×53

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

Now multiplying the highest exponent prime factors to calculate the LCM of 2000 and 2004.

LCM(2000,2004) = 24×31×53×1671
LCM(2000,2004) = 1002000

Factors of 2000

List of positive integer factors of 2000 that divides 2000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000

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

Least Common Multiple of 2000 and 2004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2000 and 2004, than apply into the LCM equation.

GCF(2000,2004) = 4
LCM(2000,2004) = ( 2000 × 2004) / 4
LCM(2000,2004) = 4008000 / 4
LCM(2000,2004) = 1002000

Properties of LCM 2000 and 2004

(i) The LCM of 2004 and 2000 is associative

LCM of 2000 and 2004 = LCM of 2004 and 2000

Related Least Common Multiples of 2000

Related Least Common Multiples of 2004

Frequently Asked Questions on LCM of 2000 and 2004

1. What is the LCM of 2000 and 2004?

Answer: LCM of 2000 and 2004 is 1002000.

2. What are the Factors of 2000?

Answer: Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. There are 20 integers that are factors of 2000. The greatest factor of 2000 is 2000.

3. 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.

4. How to Find the LCM of 2000 and 2004?

Answer:

Least Common Multiple of 2000 and 2004 = 1002000

Step 1: Find the prime factorization of 2000

2000 = 2 x 2 x 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 2004

2004 = 2 x 2 x 3 x 167

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

LCM = 1002000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 167

Step 4: Therefore, the least common multiple of 2000 and 2004 is 1002000.