Least Common Multiple of 1000 and 1005

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1000 and 1005 the smallest integer that is 201000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1005 is 201000.

LCM(1000,1005) = 201000

LCM of 1000 and 1005

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

LCM of:
and

Least Common Multiple of 1000 and 1005

LCM of 1000 and 1005 is 201000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1005. First we will calculate the prime factors of 1000 and 1005.

Prime Factorization of 1000


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

Prime factors of 1000 are 2,5. Prime factorization of 1000 in exponential form is:

1000 = 23×53

Prime Factorization of 1005


3 1005
5 335
67 67
1

Prime factors of 1005 are 3, 5,67. Prime factorization of 1005 in exponential form is:

1005 = 31×51×671

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1005.

LCM(1000,1005) = 23×31×53×671
LCM(1000,1005) = 201000

Factors of 1000

List of positive integer factors of 1000 that divides 1000 without a remainder.

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

Factors of 1005

List of positive integer factors of 1005 that divides 1005 without a remainder.

1, 3, 5, 15, 67, 201, 335, 1005

Least Common Multiple of 1000 and 1005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1000 and 1005, than apply into the LCM equation.

GCF(1000,1005) = 5
LCM(1000,1005) = ( 1000 × 1005) / 5
LCM(1000,1005) = 1005000 / 5
LCM(1000,1005) = 201000

Properties of LCM 1000 and 1005

(i) The LCM of 1005 and 1000 is associative

LCM of 1000 and 1005 = LCM of 1005 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1005

Frequently Asked Questions on LCM of 1000 and 1005

1. What is the LCM of 1000 and 1005?

Answer: LCM of 1000 and 1005 is 201000.

2. What are the Factors of 1000?

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

3. What are the Factors of 1005?

Answer: Factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005. There are 8 integers that are factors of 1005. The greatest factor of 1005 is 1005.

4. How to Find the LCM of 1000 and 1005?

Answer:

Least Common Multiple of 1000 and 1005 = 201000

Step 1: Find the prime factorization of 1000

1000 = 2 x 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 1005

1005 = 3 x 5 x 67

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

LCM = 201000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 67

Step 4: Therefore, the least common multiple of 1000 and 1005 is 201000.