Least Common Multiple of 5993 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 5993 and 6000 the smallest integer that is 35958000 that is divisible by both numbers.

Least Common Multiple (LCM) of 5993 and 6000 is 35958000.

LCM(5993,6000) = 35958000

LCM of 5993 and 6000

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

LCM of:
and

Least Common Multiple of 5993 and 6000

LCM of 5993 and 6000 is 35958000

Least common multiple can be found by multiplying the highest exponent prime factors of 5993 and 6000. First we will calculate the prime factors of 5993 and 6000.

Prime Factorization of 5993


13 5993
461 461
1

Prime factors of 5993 are 13,461. Prime factorization of 5993 in exponential form is:

5993 = 131×4611

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 5993 and 6000.

LCM(5993,6000) = 24×31×53×131×4611
LCM(5993,6000) = 35958000

Factors of 5993

List of positive integer factors of 5993 that divides 5993 without a remainder.

1, 13, 461, 5993

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 5993 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 5993 and 6000, than apply into the LCM equation.

GCF(5993,6000) = 1
LCM(5993,6000) = ( 5993 × 6000) / 1
LCM(5993,6000) = 35958000 / 1
LCM(5993,6000) = 35958000

Properties of LCM 5993 and 6000

(i) The LCM of 6000 and 5993 is associative

LCM of 5993 and 6000 = LCM of 6000 and 5993

Related Least Common Multiples of 5993

Related Least Common Multiples of 6000

Frequently Asked Questions on LCM of 5993 and 6000

1. What is the LCM of 5993 and 6000?

Answer: LCM of 5993 and 6000 is 35958000.

2. What are the Factors of 5993?

Answer: Factors of 5993 are 1, 13, 461, 5993. There are 4 integers that are factors of 5993. The greatest factor of 5993 is 5993.

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 5993 and 6000?

Answer:

Least Common Multiple of 5993 and 6000 = 35958000

Step 1: Find the prime factorization of 5993

5993 = 13 x 461

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 = 35958000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 13 x 461

Step 4: Therefore, the least common multiple of 5993 and 6000 is 35958000.