LCM of 285 and 289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 285 and 289 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 82365 as output. Here you can check the answer for Find the LCM of 285 and 289.
What is LCM of 285 and 289
Given Numbers are 285, 289
We can find the LCM of 285, 289 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 285 and 289
Multiples of 285 =285,570,855,1140,1425,1710,1995,2280,2565,2850,3135,3420,3705,3990,4275,4560,4845,
Multiples of 289 =289,578,867,1156,1445,1734,2023,2312,2601,2890,3179,3468,3757,4046,4335,4624,4913,
Now, get the least common multiple of 285, 289 which is 82365
So, the LCM of 285, 289 is 82365.
Least Common Multiple (LCM) of 285 and 289 with the help of Prime Factorisation
One method for determining the LCM of 285 and 289 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 285's prime factorization:
| 3 | 285 |
| 5 | 95 |
| 19 | 19 |
| 1 |
Prime factors of 285 are 3, 5,19.
285 = 31×51×191
And this is 289's prime factorization:
| 17 | 289 |
| 17 | 17 |
| 1 |
Prime factors of 289 are 17.
289 = 172
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3, 5,19,17
.31×51×172×191 = 82365
This shows that the LCM of 285 and 289 is 82365.
How to Calculate the LCM of 285 and 289 Using Common Multiples
The first step in determining the Least Common Multiple of 285 and 289 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 285 and 289:
Lets look at the first ten multiples of these numbers, 285 and 289:
285,570,855,1140,1425,1710,1995,2280,2565,4845 are the first ten multiples of 285.
289,578,867,1156,1445,1734,2023,2312,2601,4913 are the first ten multiples of 289.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 285 and 289, for example, are 3420, 4845, and 4624. 82365 is the least common multiple since it is the smallest.
285 and 289 have an LCM of 82365.
Least Common Multiple of 285 and 289 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 285 and 289, than apply into the LCM equation.
GCF(285,289) = 1
LCM(285,289) = ( 285 × 289) / 1
LCM(285,289) = 82365 / 1
LCM(285,289) = 82365
Related Least Common Multiples of 285
Related Least Common Multiples of 289
Frequently Asked Questions on LCM of 285 and 289
1. What is the LCM of 285 and 289?
The LCM of 285 and 289 is 82365.
2. How to find the lowest common multiple of 285 and 289?
To find the lowest common multiple of 285 and 289, we have to get the multip;es of both numbers and identify the least common multiple in them which is 82365.
3. What are the Factors of 285?
Answer: Factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285. There are 8 integers that are factors of 285. The greatest factor of 285 is 285.
4. What are the Factors of 289?
Answer: Factors of 289 are 1, 17, 289. There are 3 integers that are factors of 289. The greatest factor of 289 is 289.
5. How to Find the LCM of 285 and 289?Answer:
Least Common Multiple of 285 and 289 = 82365
Step 1: Find the prime factorization of 285
285 = 3 x 5 x 19
Step 2: Find the prime factorization of 289
289 = 17 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 82365 = 3 x 5 x 17 x 17 x 19
Step 4: Therefore, the least common multiple of 285 and 289 is 82365.