Least Common Multiple of 1000 and 1006

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 1006 the smallest integer that is 503000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1006 is 503000.

LCM(1000,1006) = 503000

LCM of 1000 and 1006

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

LCM of:
and

Least Common Multiple of 1000 and 1006

LCM of 1000 and 1006 is 503000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1006. First we will calculate the prime factors of 1000 and 1006.

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 1006


2 1006
503 503
1

Prime factors of 1006 are 2,503. Prime factorization of 1006 in exponential form is:

1006 = 21×5031

Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1006.

LCM(1000,1006) = 23×53×5031
LCM(1000,1006) = 503000

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 1006

List of positive integer factors of 1006 that divides 1006 without a remainder.

1, 2, 503, 1006

Least Common Multiple of 1000 and 1006 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 1006, than apply into the LCM equation.

GCF(1000,1006) = 2
LCM(1000,1006) = ( 1000 × 1006) / 2
LCM(1000,1006) = 1006000 / 2
LCM(1000,1006) = 503000

Properties of LCM 1000 and 1006

(i) The LCM of 1006 and 1000 is associative

LCM of 1000 and 1006 = LCM of 1006 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1006

Frequently Asked Questions on LCM of 1000 and 1006

1. What is the LCM of 1000 and 1006?

Answer: LCM of 1000 and 1006 is 503000.

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 1006?

Answer: Factors of 1006 are 1, 2, 503, 1006. There are 4 integers that are factors of 1006. The greatest factor of 1006 is 1006.

4. How to Find the LCM of 1000 and 1006?

Answer:

Least Common Multiple of 1000 and 1006 = 503000

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 1006

1006 = 2 x 503

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

LCM = 503000 = 2 x 2 x 2 x 5 x 5 x 5 x 503

Step 4: Therefore, the least common multiple of 1000 and 1006 is 503000.