Least Common Multiple of 1000 and 1004

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 1004 the smallest integer that is 251000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1004 is 251000.

LCM(1000,1004) = 251000

LCM of 1000 and 1004

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

LCM of:
and

Least Common Multiple of 1000 and 1004

LCM of 1000 and 1004 is 251000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1004. First we will calculate the prime factors of 1000 and 1004.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1004.

LCM(1000,1004) = 23×53×2511
LCM(1000,1004) = 251000

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 1004

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

1, 2, 4, 251, 502, 1004

Least Common Multiple of 1000 and 1004 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 1004, than apply into the LCM equation.

GCF(1000,1004) = 4
LCM(1000,1004) = ( 1000 × 1004) / 4
LCM(1000,1004) = 1004000 / 4
LCM(1000,1004) = 251000

Properties of LCM 1000 and 1004

(i) The LCM of 1004 and 1000 is associative

LCM of 1000 and 1004 = LCM of 1004 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1004

Frequently Asked Questions on LCM of 1000 and 1004

1. What is the LCM of 1000 and 1004?

Answer: LCM of 1000 and 1004 is 251000.

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 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.

4. How to Find the LCM of 1000 and 1004?

Answer:

Least Common Multiple of 1000 and 1004 = 251000

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 1004

1004 = 2 x 2 x 251

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

LCM = 251000 = 2 x 2 x 2 x 5 x 5 x 5 x 251

Step 4: Therefore, the least common multiple of 1000 and 1004 is 251000.