Least Common Multiple of 2000 and 2005

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 2005 the smallest integer that is 802000 that is divisible by both numbers.

Least Common Multiple (LCM) of 2000 and 2005 is 802000.

LCM(2000,2005) = 802000

LCM of 2000 and 2005

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

LCM of:
and

Least Common Multiple of 2000 and 2005

LCM of 2000 and 2005 is 802000

Least common multiple can be found by multiplying the highest exponent prime factors of 2000 and 2005. First we will calculate the prime factors of 2000 and 2005.

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 2005


5 2005
401 401
1

Prime factors of 2005 are 5,401. Prime factorization of 2005 in exponential form is:

2005 = 51×4011

Now multiplying the highest exponent prime factors to calculate the LCM of 2000 and 2005.

LCM(2000,2005) = 24×53×4011
LCM(2000,2005) = 802000

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 2005

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

1, 5, 401, 2005

Least Common Multiple of 2000 and 2005 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 2005, than apply into the LCM equation.

GCF(2000,2005) = 5
LCM(2000,2005) = ( 2000 × 2005) / 5
LCM(2000,2005) = 4010000 / 5
LCM(2000,2005) = 802000

Properties of LCM 2000 and 2005

(i) The LCM of 2005 and 2000 is associative

LCM of 2000 and 2005 = LCM of 2005 and 2000

Related Least Common Multiples of 2000

Related Least Common Multiples of 2005

Frequently Asked Questions on LCM of 2000 and 2005

1. What is the LCM of 2000 and 2005?

Answer: LCM of 2000 and 2005 is 802000.

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 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.

4. How to Find the LCM of 2000 and 2005?

Answer:

Least Common Multiple of 2000 and 2005 = 802000

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 2005

2005 = 5 x 401

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

LCM = 802000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 401

Step 4: Therefore, the least common multiple of 2000 and 2005 is 802000.