LCM of 289 and 297
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 289 and 297 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 85833 as output. Here you can check the answer for Find the LCM of 289 and 297.
What is LCM of 289 and 297
Given Numbers are 289, 297
We can find the LCM of 289, 297 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 289 and 297
Multiples of 289 =289,578,867,1156,1445,1734,2023,2312,2601,2890,3179,3468,3757,4046,4335,4624,4913,
Multiples of 297 =297,594,891,1188,1485,1782,2079,2376,2673,2970,3267,3564,3861,4158,4455,4752,5049,
Now, get the least common multiple of 289, 297 which is 85833
So, the LCM of 289, 297 is 85833.
Least Common Multiple (LCM) of 289 and 297 with the help of Prime Factorisation
One method for determining the LCM of 289 and 297 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 289's prime factorization:
| 17 | 289 |
| 17 | 17 |
| 1 |
Prime factors of 289 are 17.
289 = 172
And this is 297's prime factorization:
| 3 | 297 |
| 3 | 99 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 297 are 3,11.
297 = 33×111
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:17, 3,11
.33×111×172 = 85833
This shows that the LCM of 289 and 297 is 85833.
How to Calculate the LCM of 289 and 297 Using Common Multiples
The first step in determining the Least Common Multiple of 289 and 297 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 289 and 297:
Lets look at the first ten multiples of these numbers, 289 and 297:
289,578,867,1156,1445,1734,2023,2312,2601,4913 are the first ten multiples of 289.
297,594,891,1188,1485,1782,2079,2376,2673,5049 are the first ten multiples of 297.
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 289 and 297, for example, are 3468, 4913, and 4752. 85833 is the least common multiple since it is the smallest.
289 and 297 have an LCM of 85833.
Least Common Multiple of 289 and 297 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 289 and 297, than apply into the LCM equation.
GCF(289,297) = 1
LCM(289,297) = ( 289 × 297) / 1
LCM(289,297) = 85833 / 1
LCM(289,297) = 85833
Related Least Common Multiples of 289
Related Least Common Multiples of 297
Frequently Asked Questions on LCM of 289 and 297
1. What is the LCM of 289 and 297?
The LCM of 289 and 297 is 85833.
2. How to find the lowest common multiple of 289 and 297?
To find the lowest common multiple of 289 and 297, we have to get the multip;es of both numbers and identify the least common multiple in them which is 85833.
3. 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.
4. What are the Factors of 297?
Answer: Factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297. There are 8 integers that are factors of 297. The greatest factor of 297 is 297.
5. How to Find the LCM of 289 and 297?Answer:
Least Common Multiple of 289 and 297 = 85833
Step 1: Find the prime factorization of 289
289 = 17 x 17
Step 2: Find the prime factorization of 297
297 = 3 x 3 x 3 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 85833 = 3 x 3 x 3 x 11 x 17 x 17
Step 4: Therefore, the least common multiple of 289 and 297 is 85833.