Least Common Multiple of 585 and 588

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 588 the smallest integer that is 114660 that is divisible by both numbers.

Least Common Multiple (LCM) of 585 and 588 is 114660.

LCM(585,588) = 114660

LCM of 585 and 588

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

LCM of:
and

Least Common Multiple of 585 and 588

LCM of 585 and 588 is 114660

Least common multiple can be found by multiplying the highest exponent prime factors of 585 and 588. First we will calculate the prime factors of 585 and 588.

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 588


2 588
2 294
3 147
7 49
7 7
1

Prime factors of 588 are 2, 3,7. Prime factorization of 588 in exponential form is:

588 = 22×31×72

Now multiplying the highest exponent prime factors to calculate the LCM of 585 and 588.

LCM(585,588) = 22×32×51×72×131
LCM(585,588) = 114660

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 588

List of positive integer factors of 588 that divides 588 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588

Least Common Multiple of 585 and 588 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 588, than apply into the LCM equation.

GCF(585,588) = 3
LCM(585,588) = ( 585 × 588) / 3
LCM(585,588) = 343980 / 3
LCM(585,588) = 114660

Properties of LCM 585 and 588

(i) The LCM of 588 and 585 is associative

LCM of 585 and 588 = LCM of 588 and 585

Related Least Common Multiples of 585

Related Least Common Multiples of 588

Frequently Asked Questions on LCM of 585 and 588

1. What is the LCM of 585 and 588?

Answer: LCM of 585 and 588 is 114660.

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 588?

Answer: Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588. There are 18 integers that are factors of 588. The greatest factor of 588 is 588.

4. How to Find the LCM of 585 and 588?

Answer:

Least Common Multiple of 585 and 588 = 114660

Step 1: Find the prime factorization of 585

585 = 3 x 3 x 5 x 13

Step 2: Find the prime factorization of 588

588 = 2 x 2 x 3 x 7 x 7

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

LCM = 114660 = 2 x 2 x 3 x 3 x 5 x 7 x 7 x 13

Step 4: Therefore, the least common multiple of 585 and 588 is 114660.