Least Common Multiple of 9000 and 9006

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 9006 the smallest integer that is 13509000 that is divisible by both numbers.

Least Common Multiple (LCM) of 9000 and 9006 is 13509000.

LCM(9000,9006) = 13509000

LCM of 9000 and 9006

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

LCM of:
and

Least Common Multiple of 9000 and 9006

LCM of 9000 and 9006 is 13509000

Least common multiple can be found by multiplying the highest exponent prime factors of 9000 and 9006. First we will calculate the prime factors of 9000 and 9006.

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 9006


2 9006
3 4503
19 1501
79 79
1

Prime factors of 9006 are 2, 3, 19,79. Prime factorization of 9006 in exponential form is:

9006 = 21×31×191×791

Now multiplying the highest exponent prime factors to calculate the LCM of 9000 and 9006.

LCM(9000,9006) = 23×32×53×191×791
LCM(9000,9006) = 13509000

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 9006

List of positive integer factors of 9006 that divides 9006 without a remainder.

1, 2, 3, 6, 19, 38, 57, 79, 114, 158, 237, 474, 1501, 3002, 4503, 9006

Least Common Multiple of 9000 and 9006 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 9006, than apply into the LCM equation.

GCF(9000,9006) = 6
LCM(9000,9006) = ( 9000 × 9006) / 6
LCM(9000,9006) = 81054000 / 6
LCM(9000,9006) = 13509000

Properties of LCM 9000 and 9006

(i) The LCM of 9006 and 9000 is associative

LCM of 9000 and 9006 = LCM of 9006 and 9000

Related Least Common Multiples of 9000

Related Least Common Multiples of 9006

Frequently Asked Questions on LCM of 9000 and 9006

1. What is the LCM of 9000 and 9006?

Answer: LCM of 9000 and 9006 is 13509000.

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 9006?

Answer: Factors of 9006 are 1, 2, 3, 6, 19, 38, 57, 79, 114, 158, 237, 474, 1501, 3002, 4503, 9006. There are 16 integers that are factors of 9006. The greatest factor of 9006 is 9006.

4. How to Find the LCM of 9000 and 9006?

Answer:

Least Common Multiple of 9000 and 9006 = 13509000

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 9006

9006 = 2 x 3 x 19 x 79

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

LCM = 13509000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 19 x 79

Step 4: Therefore, the least common multiple of 9000 and 9006 is 13509000.