Least Common Multiple of 8992 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 8992 and 9000 the smallest integer that is 10116000 that is divisible by both numbers.

Least Common Multiple (LCM) of 8992 and 9000 is 10116000.

LCM(8992,9000) = 10116000

LCM of 8992 and 9000

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

LCM of:
and

Least Common Multiple of 8992 and 9000

LCM of 8992 and 9000 is 10116000

Least common multiple can be found by multiplying the highest exponent prime factors of 8992 and 9000. First we will calculate the prime factors of 8992 and 9000.

Prime Factorization of 8992


2 8992
2 4496
2 2248
2 1124
2 562
281 281
1

Prime factors of 8992 are 2,281. Prime factorization of 8992 in exponential form is:

8992 = 25×2811

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 8992 and 9000.

LCM(8992,9000) = 25×32×53×2811
LCM(8992,9000) = 10116000

Factors of 8992

List of positive integer factors of 8992 that divides 8992 without a remainder.

1, 2, 4, 8, 16, 32, 281, 562, 1124, 2248, 4496, 8992

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 8992 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 8992 and 9000, than apply into the LCM equation.

GCF(8992,9000) = 8
LCM(8992,9000) = ( 8992 × 9000) / 8
LCM(8992,9000) = 80928000 / 8
LCM(8992,9000) = 10116000

Properties of LCM 8992 and 9000

(i) The LCM of 9000 and 8992 is associative

LCM of 8992 and 9000 = LCM of 9000 and 8992

Related Least Common Multiples of 8992

Related Least Common Multiples of 9000

Frequently Asked Questions on LCM of 8992 and 9000

1. What is the LCM of 8992 and 9000?

Answer: LCM of 8992 and 9000 is 10116000.

2. What are the Factors of 8992?

Answer: Factors of 8992 are 1, 2, 4, 8, 16, 32, 281, 562, 1124, 2248, 4496, 8992. There are 12 integers that are factors of 8992. The greatest factor of 8992 is 8992.

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 8992 and 9000?

Answer:

Least Common Multiple of 8992 and 9000 = 10116000

Step 1: Find the prime factorization of 8992

8992 = 2 x 2 x 2 x 2 x 2 x 281

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 = 10116000 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 281

Step 4: Therefore, the least common multiple of 8992 and 9000 is 10116000.