Least Common Multiple of 1000 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 1000 and 1007 the smallest integer that is 1007000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1007 is 1007000.

LCM(1000,1007) = 1007000

LCM of 1000 and 1007

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

LCM of:
and

Least Common Multiple of 1000 and 1007

LCM of 1000 and 1007 is 1007000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1007. First we will calculate the prime factors of 1000 and 1007.

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 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 1000 and 1007.

LCM(1000,1007) = 23×53×191×531
LCM(1000,1007) = 1007000

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 1007

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

1, 19, 53, 1007

Least Common Multiple of 1000 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 1000 and 1007, than apply into the LCM equation.

GCF(1000,1007) = 1
LCM(1000,1007) = ( 1000 × 1007) / 1
LCM(1000,1007) = 1007000 / 1
LCM(1000,1007) = 1007000

Properties of LCM 1000 and 1007

(i) The LCM of 1007 and 1000 is associative

LCM of 1000 and 1007 = LCM of 1007 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1007

Frequently Asked Questions on LCM of 1000 and 1007

1. What is the LCM of 1000 and 1007?

Answer: LCM of 1000 and 1007 is 1007000.

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 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 1000 and 1007?

Answer:

Least Common Multiple of 1000 and 1007 = 1007000

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 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 = 1007000 = 2 x 2 x 2 x 5 x 5 x 5 x 19 x 53

Step 4: Therefore, the least common multiple of 1000 and 1007 is 1007000.