It is easy to find the LCM of 225 and 231 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 17325 as output. Here you can check the answer for Find the LCM of 225 and 231.
Given Numbers are 225, 231
We can find the LCM of 225, 231 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 225 and 231
Multiples of 225 =225,450,675,900,1125,1350,1575,1800,2025,2250,2475,2700,2925,3150,3375,3600,3825,
Multiples of 231 =231,462,693,924,1155,1386,1617,1848,2079,2310,2541,2772,3003,3234,3465,3696,3927,
Now, get the least common multiple of 225, 231 which is 17325
So, the LCM of 225, 231 is 17325.
One method for determining the LCM of 225 and 231 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 225's prime factorization:3 | 225 |
3 | 75 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 225 are 3,5.
225 = 32×52
And this is 231's prime factorization:
3 | 231 |
7 | 77 |
11 | 11 |
1 |
Prime factors of 231 are 3, 7,11.
231 = 31×71×111
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: 3,5, 7,11
.32×52×71×111 = 17325
This shows that the LCM of 225 and 231 is 17325.
The first step in determining the Least Common Multiple of 225 and 231 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 225 and 231:
Lets look at the first ten multiples of these numbers, 225 and 231:
225,450,675,900,1125,1350,1575,1800,2025,3825 are the first ten multiples of 225.
231,462,693,924,1155,1386,1617,1848,2079,3927 are the first ten multiples of 231.
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 225 and 231, for example, are 2700, 3825, and 3696. 17325 is the least common multiple since it is the smallest.
225 and 231 have an LCM of 17325.
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 225 and 231, than apply into the LCM equation.
GCF(225,231) = 3
LCM(225,231) = ( 225 × 231) / 3
LCM(225,231) = 51975 / 3
LCM(225,231) = 17325
1. What is the LCM of 225 and 231?
The LCM of 225 and 231 is 17325.
2. How to find the lowest common multiple of 225 and 231?
To find the lowest common multiple of 225 and 231, we have to get the multip;es of both numbers and identify the least common multiple in them which is 17325.
3. What are the Factors of 225?
Answer: Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225. There are 9 integers that are factors of 225. The greatest factor of 225 is 225.
4. What are the Factors of 231?
Answer: Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. There are 8 integers that are factors of 231. The greatest factor of 231 is 231.
5. How to Find the LCM of 225 and 231?Answer:
Least Common Multiple of 225 and 231 = 17325
Step 1: Find the prime factorization of 225
225 = 3 x 3 x 5 x 5
Step 2: Find the prime factorization of 231
231 = 3 x 7 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 = 17325 = 3 x 3 x 5 x 5 x 7 x 11
Step 4: Therefore, the least common multiple of 225 and 231 is 17325.