Least Common Multiple of 1002 and 1007

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 1007 the smallest integer that is 1009014 that is divisible by both numbers.

Least Common Multiple (LCM) of 1002 and 1007 is 1009014.

LCM(1002,1007) = 1009014

LCM of 1002 and 1007

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

LCM of:
and

Least Common Multiple of 1002 and 1007

LCM of 1002 and 1007 is 1009014

Least common multiple can be found by multiplying the highest exponent prime factors of 1002 and 1007. First we will calculate the prime factors of 1002 and 1007.

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 1007


19 1007
53 53
1

Prime factors of 1007 are 19,53. Prime factorization of 1007 in exponential form is:

1007 = 191×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1002 and 1007.

LCM(1002,1007) = 21×31×191×531×1671
LCM(1002,1007) = 1009014

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 1007

List of positive integer factors of 1007 that divides 1007 without a remainder.

1, 19, 53, 1007

Least Common Multiple of 1002 and 1007 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 1007, than apply into the LCM equation.

GCF(1002,1007) = 1
LCM(1002,1007) = ( 1002 × 1007) / 1
LCM(1002,1007) = 1009014 / 1
LCM(1002,1007) = 1009014

Properties of LCM 1002 and 1007

(i) The LCM of 1007 and 1002 is associative

LCM of 1002 and 1007 = LCM of 1007 and 1002

Related Least Common Multiples of 1002

Related Least Common Multiples of 1007

Frequently Asked Questions on LCM of 1002 and 1007

1. What is the LCM of 1002 and 1007?

Answer: LCM of 1002 and 1007 is 1009014.

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 1007?

Answer: Factors of 1007 are 1, 19, 53, 1007. There are 4 integers that are factors of 1007. The greatest factor of 1007 is 1007.

4. How to Find the LCM of 1002 and 1007?

Answer:

Least Common Multiple of 1002 and 1007 = 1009014

Step 1: Find the prime factorization of 1002

1002 = 2 x 3 x 167

Step 2: Find the prime factorization of 1007

1007 = 19 x 53

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

LCM = 1009014 = 2 x 3 x 19 x 53 x 167

Step 4: Therefore, the least common multiple of 1002 and 1007 is 1009014.