Least Common Multiple of 1004 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 1004 and 1005 the smallest integer that is 1009020 that is divisible by both numbers.

Least Common Multiple (LCM) of 1004 and 1005 is 1009020.

LCM(1004,1005) = 1009020

LCM of 1004 and 1005

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

LCM of:
and

Least Common Multiple of 1004 and 1005

LCM of 1004 and 1005 is 1009020

Least common multiple can be found by multiplying the highest exponent prime factors of 1004 and 1005. First we will calculate the prime factors of 1004 and 1005.

Prime Factorization of 1004


2 1004
2 502
251 251
1

Prime factors of 1004 are 2,251. Prime factorization of 1004 in exponential form is:

1004 = 22×2511

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 1004 and 1005.

LCM(1004,1005) = 22×31×51×671×2511
LCM(1004,1005) = 1009020

Factors of 1004

List of positive integer factors of 1004 that divides 1004 without a remainder.

1, 2, 4, 251, 502, 1004

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 1004 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 1004 and 1005, than apply into the LCM equation.

GCF(1004,1005) = 1
LCM(1004,1005) = ( 1004 × 1005) / 1
LCM(1004,1005) = 1009020 / 1
LCM(1004,1005) = 1009020

Properties of LCM 1004 and 1005

(i) The LCM of 1005 and 1004 is associative

LCM of 1004 and 1005 = LCM of 1005 and 1004

Related Least Common Multiples of 1004

Related Least Common Multiples of 1005

Frequently Asked Questions on LCM of 1004 and 1005

1. What is the LCM of 1004 and 1005?

Answer: LCM of 1004 and 1005 is 1009020.

2. What are the Factors of 1004?

Answer: Factors of 1004 are 1, 2, 4, 251, 502, 1004. There are 6 integers that are factors of 1004. The greatest factor of 1004 is 1004.

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 1004 and 1005?

Answer:

Least Common Multiple of 1004 and 1005 = 1009020

Step 1: Find the prime factorization of 1004

1004 = 2 x 2 x 251

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 = 1009020 = 2 x 2 x 3 x 5 x 67 x 251

Step 4: Therefore, the least common multiple of 1004 and 1005 is 1009020.