Least Common Multiple of 585 and 590

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 590 the smallest integer that is 69030 that is divisible by both numbers.

Least Common Multiple (LCM) of 585 and 590 is 69030.

LCM(585,590) = 69030

LCM of 585 and 590

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

LCM of:
and

Least Common Multiple of 585 and 590

LCM of 585 and 590 is 69030

Least common multiple can be found by multiplying the highest exponent prime factors of 585 and 590. First we will calculate the prime factors of 585 and 590.

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 590


2 590
5 295
59 59
1

Prime factors of 590 are 2, 5,59. Prime factorization of 590 in exponential form is:

590 = 21×51×591

Now multiplying the highest exponent prime factors to calculate the LCM of 585 and 590.

LCM(585,590) = 21×32×51×131×591
LCM(585,590) = 69030

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 590

List of positive integer factors of 590 that divides 590 without a remainder.

1, 2, 5, 10, 59, 118, 295, 590

Least Common Multiple of 585 and 590 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 590, than apply into the LCM equation.

GCF(585,590) = 5
LCM(585,590) = ( 585 × 590) / 5
LCM(585,590) = 345150 / 5
LCM(585,590) = 69030

Properties of LCM 585 and 590

(i) The LCM of 590 and 585 is associative

LCM of 585 and 590 = LCM of 590 and 585

Related Least Common Multiples of 585

Related Least Common Multiples of 590

Frequently Asked Questions on LCM of 585 and 590

1. What is the LCM of 585 and 590?

Answer: LCM of 585 and 590 is 69030.

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 590?

Answer: Factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590. There are 8 integers that are factors of 590. The greatest factor of 590 is 590.

4. How to Find the LCM of 585 and 590?

Answer:

Least Common Multiple of 585 and 590 = 69030

Step 1: Find the prime factorization of 585

585 = 3 x 3 x 5 x 13

Step 2: Find the prime factorization of 590

590 = 2 x 5 x 59

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

LCM = 69030 = 2 x 3 x 3 x 5 x 13 x 59

Step 4: Therefore, the least common multiple of 585 and 590 is 69030.