Least Common Multiple of 1002 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 1002 and 1003 the smallest integer that is 1005006 that is divisible by both numbers.

Least Common Multiple (LCM) of 1002 and 1003 is 1005006.

LCM(1002,1003) = 1005006

LCM of 1002 and 1003

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

LCM of:
and

Least Common Multiple of 1002 and 1003

LCM of 1002 and 1003 is 1005006

Least common multiple can be found by multiplying the highest exponent prime factors of 1002 and 1003. First we will calculate the prime factors of 1002 and 1003.

Prime Factorization of 1002


2 1002
3 501
167 167
1

Prime factors of 1002 are 2, 3,167. Prime factorization of 1002 in exponential form is:

1002 = 21×31×1671

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 1002 and 1003.

LCM(1002,1003) = 21×31×171×591×1671
LCM(1002,1003) = 1005006

Factors of 1002

List of positive integer factors of 1002 that divides 1002 without a remainder.

1, 2, 3, 6, 167, 334, 501, 1002

Factors of 1003

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

1, 17, 59, 1003

Least Common Multiple of 1002 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 1002 and 1003, than apply into the LCM equation.

GCF(1002,1003) = 1
LCM(1002,1003) = ( 1002 × 1003) / 1
LCM(1002,1003) = 1005006 / 1
LCM(1002,1003) = 1005006

Properties of LCM 1002 and 1003

(i) The LCM of 1003 and 1002 is associative

LCM of 1002 and 1003 = LCM of 1003 and 1002

Related Least Common Multiples of 1002

Related Least Common Multiples of 1003

Frequently Asked Questions on LCM of 1002 and 1003

1. What is the LCM of 1002 and 1003?

Answer: LCM of 1002 and 1003 is 1005006.

2. What are the Factors of 1002?

Answer: Factors of 1002 are 1, 2, 3, 6, 167, 334, 501, 1002. There are 8 integers that are factors of 1002. The greatest factor of 1002 is 1002.

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 1002 and 1003?

Answer:

Least Common Multiple of 1002 and 1003 = 1005006

Step 1: Find the prime factorization of 1002

1002 = 2 x 3 x 167

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 = 1005006 = 2 x 3 x 17 x 59 x 167

Step 4: Therefore, the least common multiple of 1002 and 1003 is 1005006.