Least Common Multiple of 9000 and 9003

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9000 and 9003 the smallest integer that is 27009000 that is divisible by both numbers.

Least Common Multiple (LCM) of 9000 and 9003 is 27009000.

LCM(9000,9003) = 27009000

LCM of 9000 and 9003

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

LCM of:
and

Least Common Multiple of 9000 and 9003

LCM of 9000 and 9003 is 27009000

Least common multiple can be found by multiplying the highest exponent prime factors of 9000 and 9003. First we will calculate the prime factors of 9000 and 9003.

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

Prime Factorization of 9003


3 9003
3001 3001
1

Prime factors of 9003 are 3,3001. Prime factorization of 9003 in exponential form is:

9003 = 31×30011

Now multiplying the highest exponent prime factors to calculate the LCM of 9000 and 9003.

LCM(9000,9003) = 23×32×53×30011
LCM(9000,9003) = 27009000

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

Factors of 9003

List of positive integer factors of 9003 that divides 9003 without a remainder.

1, 3, 3001, 9003

Least Common Multiple of 9000 and 9003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9000 and 9003, than apply into the LCM equation.

GCF(9000,9003) = 3
LCM(9000,9003) = ( 9000 × 9003) / 3
LCM(9000,9003) = 81027000 / 3
LCM(9000,9003) = 27009000

Properties of LCM 9000 and 9003

(i) The LCM of 9003 and 9000 is associative

LCM of 9000 and 9003 = LCM of 9003 and 9000

Related Least Common Multiples of 9000

Related Least Common Multiples of 9003

Frequently Asked Questions on LCM of 9000 and 9003

1. What is the LCM of 9000 and 9003?

Answer: LCM of 9000 and 9003 is 27009000.

2. 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.

3. What are the Factors of 9003?

Answer: Factors of 9003 are 1, 3, 3001, 9003. There are 4 integers that are factors of 9003. The greatest factor of 9003 is 9003.

4. How to Find the LCM of 9000 and 9003?

Answer:

Least Common Multiple of 9000 and 9003 = 27009000

Step 1: Find the prime factorization of 9000

9000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 9003

9003 = 3 x 3001

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

LCM = 27009000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 3001

Step 4: Therefore, the least common multiple of 9000 and 9003 is 27009000.