Least Common Multiple of 585 and 586

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 586 the smallest integer that is 342810 that is divisible by both numbers.

Least Common Multiple (LCM) of 585 and 586 is 342810.

LCM(585,586) = 342810

LCM of 585 and 586

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

LCM of:
and

Least Common Multiple of 585 and 586

LCM of 585 and 586 is 342810

Least common multiple can be found by multiplying the highest exponent prime factors of 585 and 586. First we will calculate the prime factors of 585 and 586.

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 586


2 586
293 293
1

Prime factors of 586 are 2,293. Prime factorization of 586 in exponential form is:

586 = 21×2931

Now multiplying the highest exponent prime factors to calculate the LCM of 585 and 586.

LCM(585,586) = 21×32×51×131×2931
LCM(585,586) = 342810

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 586

List of positive integer factors of 586 that divides 586 without a remainder.

1, 2, 293, 586

Least Common Multiple of 585 and 586 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 586, than apply into the LCM equation.

GCF(585,586) = 1
LCM(585,586) = ( 585 × 586) / 1
LCM(585,586) = 342810 / 1
LCM(585,586) = 342810

Properties of LCM 585 and 586

(i) The LCM of 586 and 585 is associative

LCM of 585 and 586 = LCM of 586 and 585

Related Least Common Multiples of 585

Related Least Common Multiples of 586

Frequently Asked Questions on LCM of 585 and 586

1. What is the LCM of 585 and 586?

Answer: LCM of 585 and 586 is 342810.

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 586?

Answer: Factors of 586 are 1, 2, 293, 586. There are 4 integers that are factors of 586. The greatest factor of 586 is 586.

4. How to Find the LCM of 585 and 586?

Answer:

Least Common Multiple of 585 and 586 = 342810

Step 1: Find the prime factorization of 585

585 = 3 x 3 x 5 x 13

Step 2: Find the prime factorization of 586

586 = 2 x 293

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

LCM = 342810 = 2 x 3 x 3 x 5 x 13 x 293

Step 4: Therefore, the least common multiple of 585 and 586 is 342810.