Least Common Multiple of 1002 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 1002 and 1005 the smallest integer that is 335670 that is divisible by both numbers.

Least Common Multiple (LCM) of 1002 and 1005 is 335670.

LCM(1002,1005) = 335670

LCM of 1002 and 1005

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

LCM of:
and

Least Common Multiple of 1002 and 1005

LCM of 1002 and 1005 is 335670

Least common multiple can be found by multiplying the highest exponent prime factors of 1002 and 1005. First we will calculate the prime factors of 1002 and 1005.

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 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 1002 and 1005.

LCM(1002,1005) = 21×31×51×671×1671
LCM(1002,1005) = 335670

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 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 1002 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 1002 and 1005, than apply into the LCM equation.

GCF(1002,1005) = 3
LCM(1002,1005) = ( 1002 × 1005) / 3
LCM(1002,1005) = 1007010 / 3
LCM(1002,1005) = 335670

Properties of LCM 1002 and 1005

(i) The LCM of 1005 and 1002 is associative

LCM of 1002 and 1005 = LCM of 1005 and 1002

Related Least Common Multiples of 1002

Related Least Common Multiples of 1005

Frequently Asked Questions on LCM of 1002 and 1005

1. What is the LCM of 1002 and 1005?

Answer: LCM of 1002 and 1005 is 335670.

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 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 1002 and 1005?

Answer:

Least Common Multiple of 1002 and 1005 = 335670

Step 1: Find the prime factorization of 1002

1002 = 2 x 3 x 167

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 = 335670 = 2 x 3 x 5 x 67 x 167

Step 4: Therefore, the least common multiple of 1002 and 1005 is 335670.