Least Common Multiple of 5985 and 5992

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5985 and 5992 the smallest integer that is 5123160 that is divisible by both numbers.

Least Common Multiple (LCM) of 5985 and 5992 is 5123160.

LCM(5985,5992) = 5123160

LCM of 5985 and 5992

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

LCM of:
and

Least Common Multiple of 5985 and 5992

LCM of 5985 and 5992 is 5123160

Least common multiple can be found by multiplying the highest exponent prime factors of 5985 and 5992. First we will calculate the prime factors of 5985 and 5992.

Prime Factorization of 5985


3 5985
3 1995
5 665
7 133
19 19
1

Prime factors of 5985 are 3, 5, 7,19. Prime factorization of 5985 in exponential form is:

5985 = 32×51×71×191

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

Now multiplying the highest exponent prime factors to calculate the LCM of 5985 and 5992.

LCM(5985,5992) = 23×32×51×71×191×1071
LCM(5985,5992) = 5123160

Factors of 5985

List of positive integer factors of 5985 that divides 5985 without a remainder.

1, 3, 5, 7, 9, 15, 19, 21, 35, 45, 57, 63, 95, 105, 133, 171, 285, 315, 399, 665, 855, 1197, 1995, 5985

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

Least Common Multiple of 5985 and 5992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5985 and 5992, than apply into the LCM equation.

GCF(5985,5992) = 7
LCM(5985,5992) = ( 5985 × 5992) / 7
LCM(5985,5992) = 35862120 / 7
LCM(5985,5992) = 5123160

Properties of LCM 5985 and 5992

(i) The LCM of 5992 and 5985 is associative

LCM of 5985 and 5992 = LCM of 5992 and 5985

Related Least Common Multiples of 5985

Related Least Common Multiples of 5992

Frequently Asked Questions on LCM of 5985 and 5992

1. What is the LCM of 5985 and 5992?

Answer: LCM of 5985 and 5992 is 5123160.

2. What are the Factors of 5985?

Answer: Factors of 5985 are 1, 3, 5, 7, 9, 15, 19, 21, 35, 45, 57, 63, 95, 105, 133, 171, 285, 315, 399, 665, 855, 1197, 1995, 5985. There are 24 integers that are factors of 5985. The greatest factor of 5985 is 5985.

3. 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.

4. How to Find the LCM of 5985 and 5992?

Answer:

Least Common Multiple of 5985 and 5992 = 5123160

Step 1: Find the prime factorization of 5985

5985 = 3 x 3 x 5 x 7 x 19

Step 2: Find the prime factorization of 5992

5992 = 2 x 2 x 2 x 7 x 107

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

LCM = 5123160 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 19 x 107

Step 4: Therefore, the least common multiple of 5985 and 5992 is 5123160.