Least Common Multiple of 999 and 1000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 999 and 1000 the smallest integer that is 999000 that is divisible by both numbers.

Least Common Multiple (LCM) of 999 and 1000 is 999000.

LCM(999,1000) = 999000

LCM of 999 and 1000

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

LCM of:
and

Least Common Multiple of 999 and 1000

LCM of 999 and 1000 is 999000

Least common multiple can be found by multiplying the highest exponent prime factors of 999 and 1000. First we will calculate the prime factors of 999 and 1000.

Prime Factorization of 999


3 999
3 333
3 111
37 37
1

Prime factors of 999 are 3,37. Prime factorization of 999 in exponential form is:

999 = 33×371

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

Now multiplying the highest exponent prime factors to calculate the LCM of 999 and 1000.

LCM(999,1000) = 23×33×53×371
LCM(999,1000) = 999000

Factors of 999

List of positive integer factors of 999 that divides 999 without a remainder.

1, 3, 9, 27, 37, 111, 333, 999

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

Least Common Multiple of 999 and 1000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 999 and 1000, than apply into the LCM equation.

GCF(999,1000) = 1
LCM(999,1000) = ( 999 × 1000) / 1
LCM(999,1000) = 999000 / 1
LCM(999,1000) = 999000

Properties of LCM 999 and 1000

(i) The LCM of 1000 and 999 is associative

LCM of 999 and 1000 = LCM of 1000 and 999

Related Least Common Multiples of 999

Related Least Common Multiples of 1000

Frequently Asked Questions on LCM of 999 and 1000

1. What is the LCM of 999 and 1000?

Answer: LCM of 999 and 1000 is 999000.

2. What are the Factors of 999?

Answer: Factors of 999 are 1, 3, 9, 27, 37, 111, 333, 999. There are 8 integers that are factors of 999. The greatest factor of 999 is 999.

3. 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.

4. How to Find the LCM of 999 and 1000?

Answer:

Least Common Multiple of 999 and 1000 = 999000

Step 1: Find the prime factorization of 999

999 = 3 x 3 x 3 x 37

Step 2: Find the prime factorization of 1000

1000 = 2 x 2 x 2 x 5 x 5 x 5

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

LCM = 999000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 37

Step 4: Therefore, the least common multiple of 999 and 1000 is 999000.