Least Common Multiple of 8993 and 9000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8993 and 9000 the smallest integer that is 80937000 that is divisible by both numbers.

Least Common Multiple (LCM) of 8993 and 9000 is 80937000.

LCM(8993,9000) = 80937000

LCM of 8993 and 9000

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

LCM of:
and

Least Common Multiple of 8993 and 9000

LCM of 8993 and 9000 is 80937000

Least common multiple can be found by multiplying the highest exponent prime factors of 8993 and 9000. First we will calculate the prime factors of 8993 and 9000.

Prime Factorization of 8993


17 8993
23 529
23 23
1

Prime factors of 8993 are 17,23. Prime factorization of 8993 in exponential form is:

8993 = 171×232

Prime Factorization of 9000


2 9000
2 4500
2 2250
3 1125
3 375
5 125
5 25
5 5
1

Prime factors of 9000 are 2, 3,5. Prime factorization of 9000 in exponential form is:

9000 = 23×32×53

Now multiplying the highest exponent prime factors to calculate the LCM of 8993 and 9000.

LCM(8993,9000) = 23×32×53×171×232
LCM(8993,9000) = 80937000

Factors of 8993

List of positive integer factors of 8993 that divides 8993 without a remainder.

1, 17, 23, 391, 529, 8993

Factors of 9000

List of positive integer factors of 9000 that divides 9000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000

Least Common Multiple of 8993 and 9000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8993 and 9000, than apply into the LCM equation.

GCF(8993,9000) = 1
LCM(8993,9000) = ( 8993 × 9000) / 1
LCM(8993,9000) = 80937000 / 1
LCM(8993,9000) = 80937000

Properties of LCM 8993 and 9000

(i) The LCM of 9000 and 8993 is associative

LCM of 8993 and 9000 = LCM of 9000 and 8993

Related Least Common Multiples of 8993

Related Least Common Multiples of 9000

Frequently Asked Questions on LCM of 8993 and 9000

1. What is the LCM of 8993 and 9000?

Answer: LCM of 8993 and 9000 is 80937000.

2. What are the Factors of 8993?

Answer: Factors of 8993 are 1, 17, 23, 391, 529, 8993. There are 6 integers that are factors of 8993. The greatest factor of 8993 is 8993.

3. What are the Factors of 9000?

Answer: Factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000. There are 48 integers that are factors of 9000. The greatest factor of 9000 is 9000.

4. How to Find the LCM of 8993 and 9000?

Answer:

Least Common Multiple of 8993 and 9000 = 80937000

Step 1: Find the prime factorization of 8993

8993 = 17 x 23 x 23

Step 2: Find the prime factorization of 9000

9000 = 2 x 2 x 2 x 3 x 3 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 = 80937000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 17 x 23 x 23

Step 4: Therefore, the least common multiple of 8993 and 9000 is 80937000.