Least Common Multiple of 1000 and 1002

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 1002 the smallest integer that is 501000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1002 is 501000.

LCM(1000,1002) = 501000

LCM of 1000 and 1002

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

LCM of:
and

Least Common Multiple of 1000 and 1002

LCM of 1000 and 1002 is 501000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1002. First we will calculate the prime factors of 1000 and 1002.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1002.

LCM(1000,1002) = 23×31×53×1671
LCM(1000,1002) = 501000

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 1002

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

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

Least Common Multiple of 1000 and 1002 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 1002, than apply into the LCM equation.

GCF(1000,1002) = 2
LCM(1000,1002) = ( 1000 × 1002) / 2
LCM(1000,1002) = 1002000 / 2
LCM(1000,1002) = 501000

Properties of LCM 1000 and 1002

(i) The LCM of 1002 and 1000 is associative

LCM of 1000 and 1002 = LCM of 1002 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1002

Frequently Asked Questions on LCM of 1000 and 1002

1. What is the LCM of 1000 and 1002?

Answer: LCM of 1000 and 1002 is 501000.

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 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.

4. How to Find the LCM of 1000 and 1002?

Answer:

Least Common Multiple of 1000 and 1002 = 501000

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 1002

1002 = 2 x 3 x 167

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

LCM = 501000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 167

Step 4: Therefore, the least common multiple of 1000 and 1002 is 501000.