Least Common Multiple of 585 and 589
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 589 the smallest integer that is 344565 that is divisible by both numbers.
Least Common Multiple (LCM) of 585 and 589 is 344565.
LCM(585,589) = 344565
LCM of 585 and 589
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 585 and 589 by Prime method
- Least Common Multiple of 585 and 589 with GCF Formula
LCM of 585 and 589 is 344565
Least common multiple can be found by multiplying the highest exponent prime factors of 585 and 589. First we will calculate the prime factors of 585 and 589.
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 589
| 19 | 589 |
| 31 | 31 |
| 1 |
Prime factors of 589 are 19,31. Prime factorization of 589 in exponential form is:
589 = 191×311
Now multiplying the highest exponent prime factors to calculate the LCM of 585 and 589.
LCM(585,589) = 32×51×131×191×311
LCM(585,589) = 344565
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 589
List of positive integer factors of 589 that divides 589 without a remainder.
1, 19, 31, 589
Least Common Multiple of 585 and 589 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 589, than apply into the LCM equation.
GCF(585,589) = 1
LCM(585,589) = ( 585 × 589) / 1
LCM(585,589) = 344565 / 1
LCM(585,589) = 344565
Properties of LCM 585 and 589
(i) The LCM of 589 and 585 is associative
LCM of 585 and 589 = LCM of 589 and 585
Related Least Common Multiples of 585
Related Least Common Multiples of 589
Frequently Asked Questions on LCM of 585 and 589
1. What is the LCM of 585 and 589?
Answer: LCM of 585 and 589 is 344565.
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 589?
Answer: Factors of 589 are 1, 19, 31, 589. There are 4 integers that are factors of 589. The greatest factor of 589 is 589.
4. How to Find the LCM of 585 and 589?
Answer:
Least Common Multiple of 585 and 589 = 344565
Step 1: Find the prime factorization of 585
585 = 3 x 3 x 5 x 13
Step 2: Find the prime factorization of 589
589 = 19 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 344565 = 3 x 3 x 5 x 13 x 19 x 31
Step 4: Therefore, the least common multiple of 585 and 589 is 344565.
