Least Common Multiple of 585 and 592

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 585 and 592 the smallest integer that is 346320 that is divisible by both numbers.

Least Common Multiple (LCM) of 585 and 592 is 346320.

LCM(585,592) = 346320

LCM of 585 and 592

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

LCM of:
and

Least Common Multiple of 585 and 592

LCM of 585 and 592 is 346320

Least common multiple can be found by multiplying the highest exponent prime factors of 585 and 592. First we will calculate the prime factors of 585 and 592.

Prime Factorization of 585


3 585
3 195
5 65
13 13
1

Prime factors of 585 are 3, 5,13. Prime factorization of 585 in exponential form is:

585 = 32×51×131

Prime Factorization of 592


2 592
2 296
2 148
2 74
37 37
1

Prime factors of 592 are 2,37. Prime factorization of 592 in exponential form is:

592 = 24×371

Now multiplying the highest exponent prime factors to calculate the LCM of 585 and 592.

LCM(585,592) = 24×32×51×131×371
LCM(585,592) = 346320

Factors of 585

List of positive integer factors of 585 that divides 585 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585

Factors of 592

List of positive integer factors of 592 that divides 592 without a remainder.

1, 2, 4, 8, 16, 37, 74, 148, 296, 592

Least Common Multiple of 585 and 592 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 585 and 592, than apply into the LCM equation.

GCF(585,592) = 1
LCM(585,592) = ( 585 × 592) / 1
LCM(585,592) = 346320 / 1
LCM(585,592) = 346320

Properties of LCM 585 and 592

(i) The LCM of 592 and 585 is associative

LCM of 585 and 592 = LCM of 592 and 585

Related Least Common Multiples of 585

Related Least Common Multiples of 592

Frequently Asked Questions on LCM of 585 and 592

1. What is the LCM of 585 and 592?

Answer: LCM of 585 and 592 is 346320.

2. What are the Factors of 585?

Answer: Factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585. There are 12 integers that are factors of 585. The greatest factor of 585 is 585.

3. What are the Factors of 592?

Answer: Factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592. There are 10 integers that are factors of 592. The greatest factor of 592 is 592.

4. How to Find the LCM of 585 and 592?

Answer:

Least Common Multiple of 585 and 592 = 346320

Step 1: Find the prime factorization of 585

585 = 3 x 3 x 5 x 13

Step 2: Find the prime factorization of 592

592 = 2 x 2 x 2 x 2 x 37

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

LCM = 346320 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13 x 37

Step 4: Therefore, the least common multiple of 585 and 592 is 346320.