Least Common Multiple of 1000 and 1003

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 1003 the smallest integer that is 1003000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1003 is 1003000.

LCM(1000,1003) = 1003000

LCM of 1000 and 1003

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

LCM of:
and

Least Common Multiple of 1000 and 1003

LCM of 1000 and 1003 is 1003000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1003. First we will calculate the prime factors of 1000 and 1003.

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 1003


17 1003
59 59
1

Prime factors of 1003 are 17,59. Prime factorization of 1003 in exponential form is:

1003 = 171×591

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1003.

LCM(1000,1003) = 23×53×171×591
LCM(1000,1003) = 1003000

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 1003

List of positive integer factors of 1003 that divides 1003 without a remainder.

1, 17, 59, 1003

Least Common Multiple of 1000 and 1003 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 1003, than apply into the LCM equation.

GCF(1000,1003) = 1
LCM(1000,1003) = ( 1000 × 1003) / 1
LCM(1000,1003) = 1003000 / 1
LCM(1000,1003) = 1003000

Properties of LCM 1000 and 1003

(i) The LCM of 1003 and 1000 is associative

LCM of 1000 and 1003 = LCM of 1003 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1003

Frequently Asked Questions on LCM of 1000 and 1003

1. What is the LCM of 1000 and 1003?

Answer: LCM of 1000 and 1003 is 1003000.

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 1003?

Answer: Factors of 1003 are 1, 17, 59, 1003. There are 4 integers that are factors of 1003. The greatest factor of 1003 is 1003.

4. How to Find the LCM of 1000 and 1003?

Answer:

Least Common Multiple of 1000 and 1003 = 1003000

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 1003

1003 = 17 x 59

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

LCM = 1003000 = 2 x 2 x 2 x 5 x 5 x 5 x 17 x 59

Step 4: Therefore, the least common multiple of 1000 and 1003 is 1003000.