LCM of 282 and 289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 282 and 289 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 81498 as output. Here you can check the answer for Find the LCM of 282 and 289.
What is LCM of 282 and 289
Given Numbers are 282, 289
We can find the LCM of 282, 289 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 282 and 289
Multiples of 282 =282,564,846,1128,1410,1692,1974,2256,2538,2820,3102,3384,3666,3948,4230,4512,4794,
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 282, 289 which is 81498
So, the LCM of 282, 289 is 81498.
Least Common Multiple (LCM) of 282 and 289 with the help of Prime Factorisation
One method for determining the LCM of 282 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 282's prime factorization:
| 2 | 282 |
| 3 | 141 |
| 47 | 47 |
| 1 |
Prime factors of 282 are 2, 3,47.
282 = 21×31×471
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: 2, 3,47,17
.21×31×172×471 = 81498
This shows that the LCM of 282 and 289 is 81498.
How to Calculate the LCM of 282 and 289 Using Common Multiples
The first step in determining the Least Common Multiple of 282 and 289 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 282 and 289:
Lets look at the first ten multiples of these numbers, 282 and 289:
282,564,846,1128,1410,1692,1974,2256,2538,4794 are the first ten multiples of 282.
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 282 and 289, for example, are 3384, 4794, and 4624. 81498 is the least common multiple since it is the smallest.
282 and 289 have an LCM of 81498.
Least Common Multiple of 282 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 282 and 289, than apply into the LCM equation.
GCF(282,289) = 1
LCM(282,289) = ( 282 × 289) / 1
LCM(282,289) = 81498 / 1
LCM(282,289) = 81498
Related Least Common Multiples of 282
Related Least Common Multiples of 289
Frequently Asked Questions on LCM of 282 and 289
1. What is the LCM of 282 and 289?
The LCM of 282 and 289 is 81498.
2. How to find the lowest common multiple of 282 and 289?
To find the lowest common multiple of 282 and 289, we have to get the multip;es of both numbers and identify the least common multiple in them which is 81498.
3. What are the Factors of 282?
Answer: Factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282. There are 8 integers that are factors of 282. The greatest factor of 282 is 282.
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 282 and 289?Answer:
Least Common Multiple of 282 and 289 = 81498
Step 1: Find the prime factorization of 282
282 = 2 x 3 x 47
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 = 81498 = 2 x 3 x 17 x 17 x 47
Step 4: Therefore, the least common multiple of 282 and 289 is 81498.