Least Common Multiple of 578 and 585

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 578 and 585 the smallest integer that is 338130 that is divisible by both numbers.

Least Common Multiple (LCM) of 578 and 585 is 338130.

LCM(578,585) = 338130

LCM of 578 and 585

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

LCM of:
and

Least Common Multiple of 578 and 585

LCM of 578 and 585 is 338130

Least common multiple can be found by multiplying the highest exponent prime factors of 578 and 585. First we will calculate the prime factors of 578 and 585.

Prime Factorization of 578


2 578
17 289
17 17
1

Prime factors of 578 are 2,17. Prime factorization of 578 in exponential form is:

578 = 21×172

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

Now multiplying the highest exponent prime factors to calculate the LCM of 578 and 585.

LCM(578,585) = 21×32×51×131×172
LCM(578,585) = 338130

Factors of 578

List of positive integer factors of 578 that divides 578 without a remainder.

1, 2, 17, 34, 289, 578

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

Least Common Multiple of 578 and 585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 578 and 585, than apply into the LCM equation.

GCF(578,585) = 1
LCM(578,585) = ( 578 × 585) / 1
LCM(578,585) = 338130 / 1
LCM(578,585) = 338130

Properties of LCM 578 and 585

(i) The LCM of 585 and 578 is associative

LCM of 578 and 585 = LCM of 585 and 578

Related Least Common Multiples of 578

Related Least Common Multiples of 585

Frequently Asked Questions on LCM of 578 and 585

1. What is the LCM of 578 and 585?

Answer: LCM of 578 and 585 is 338130.

2. What are the Factors of 578?

Answer: Factors of 578 are 1, 2, 17, 34, 289, 578. There are 6 integers that are factors of 578. The greatest factor of 578 is 578.

3. 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.

4. How to Find the LCM of 578 and 585?

Answer:

Least Common Multiple of 578 and 585 = 338130

Step 1: Find the prime factorization of 578

578 = 2 x 17 x 17

Step 2: Find the prime factorization of 585

585 = 3 x 3 x 5 x 13

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

LCM = 338130 = 2 x 3 x 3 x 5 x 13 x 17 x 17

Step 4: Therefore, the least common multiple of 578 and 585 is 338130.