Least Common Multiple of 5994 and 6000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5994 and 6000 the smallest integer that is 5994000 that is divisible by both numbers.

Least Common Multiple (LCM) of 5994 and 6000 is 5994000.

LCM(5994,6000) = 5994000

LCM of 5994 and 6000

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

LCM of:
and

Least Common Multiple of 5994 and 6000

LCM of 5994 and 6000 is 5994000

Least common multiple can be found by multiplying the highest exponent prime factors of 5994 and 6000. First we will calculate the prime factors of 5994 and 6000.

Prime Factorization of 5994


2 5994
3 2997
3 999
3 333
3 111
37 37
1

Prime factors of 5994 are 2, 3,37. Prime factorization of 5994 in exponential form is:

5994 = 21×34×371

Prime Factorization of 6000


2 6000
2 3000
2 1500
2 750
3 375
5 125
5 25
5 5
1

Prime factors of 6000 are 2, 3,5. Prime factorization of 6000 in exponential form is:

6000 = 24×31×53

Now multiplying the highest exponent prime factors to calculate the LCM of 5994 and 6000.

LCM(5994,6000) = 24×34×53×371
LCM(5994,6000) = 5994000

Factors of 5994

List of positive integer factors of 5994 that divides 5994 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 162, 222, 333, 666, 999, 1998, 2997, 5994

Factors of 6000

List of positive integer factors of 6000 that divides 6000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000

Least Common Multiple of 5994 and 6000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5994 and 6000, than apply into the LCM equation.

GCF(5994,6000) = 6
LCM(5994,6000) = ( 5994 × 6000) / 6
LCM(5994,6000) = 35964000 / 6
LCM(5994,6000) = 5994000

Properties of LCM 5994 and 6000

(i) The LCM of 6000 and 5994 is associative

LCM of 5994 and 6000 = LCM of 6000 and 5994

Related Least Common Multiples of 5994

Related Least Common Multiples of 6000

Frequently Asked Questions on LCM of 5994 and 6000

1. What is the LCM of 5994 and 6000?

Answer: LCM of 5994 and 6000 is 5994000.

2. What are the Factors of 5994?

Answer: Factors of 5994 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 162, 222, 333, 666, 999, 1998, 2997, 5994. There are 20 integers that are factors of 5994. The greatest factor of 5994 is 5994.

3. What are the Factors of 6000?

Answer: Factors of 6000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000. There are 40 integers that are factors of 6000. The greatest factor of 6000 is 6000.

4. How to Find the LCM of 5994 and 6000?

Answer:

Least Common Multiple of 5994 and 6000 = 5994000

Step 1: Find the prime factorization of 5994

5994 = 2 x 3 x 3 x 3 x 3 x 37

Step 2: Find the prime factorization of 6000

6000 = 2 x 2 x 2 x 2 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 = 5994000 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 x 5 x 37

Step 4: Therefore, the least common multiple of 5994 and 6000 is 5994000.