Least Common Multiple of 5992 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 5992 and 6000 the smallest integer that is 4494000 that is divisible by both numbers.

Least Common Multiple (LCM) of 5992 and 6000 is 4494000.

LCM(5992,6000) = 4494000

LCM of 5992 and 6000

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

LCM of:
and

Least Common Multiple of 5992 and 6000

LCM of 5992 and 6000 is 4494000

Least common multiple can be found by multiplying the highest exponent prime factors of 5992 and 6000. First we will calculate the prime factors of 5992 and 6000.

Prime Factorization of 5992


2 5992
2 2996
2 1498
7 749
107 107
1

Prime factors of 5992 are 2, 7,107. Prime factorization of 5992 in exponential form is:

5992 = 23×71×1071

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 5992 and 6000.

LCM(5992,6000) = 24×31×53×71×1071
LCM(5992,6000) = 4494000

Factors of 5992

List of positive integer factors of 5992 that divides 5992 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 107, 214, 428, 749, 856, 1498, 2996, 5992

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 5992 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 5992 and 6000, than apply into the LCM equation.

GCF(5992,6000) = 8
LCM(5992,6000) = ( 5992 × 6000) / 8
LCM(5992,6000) = 35952000 / 8
LCM(5992,6000) = 4494000

Properties of LCM 5992 and 6000

(i) The LCM of 6000 and 5992 is associative

LCM of 5992 and 6000 = LCM of 6000 and 5992

Related Least Common Multiples of 5992

Related Least Common Multiples of 6000

Frequently Asked Questions on LCM of 5992 and 6000

1. What is the LCM of 5992 and 6000?

Answer: LCM of 5992 and 6000 is 4494000.

2. What are the Factors of 5992?

Answer: Factors of 5992 are 1, 2, 4, 7, 8, 14, 28, 56, 107, 214, 428, 749, 856, 1498, 2996, 5992. There are 16 integers that are factors of 5992. The greatest factor of 5992 is 5992.

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 5992 and 6000?

Answer:

Least Common Multiple of 5992 and 6000 = 4494000

Step 1: Find the prime factorization of 5992

5992 = 2 x 2 x 2 x 7 x 107

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 = 4494000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7 x 107

Step 4: Therefore, the least common multiple of 5992 and 6000 is 4494000.