LCM of 459 and 465
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 459 and 465 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 71145 as output. Here you can check the answer for Find the LCM of 459 and 465.
What is LCM of 459 and 465
Given Numbers are 459, 465
We can find the LCM of 459, 465 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 459 and 465
Multiples of 459 =459,918,1377,1836,2295,2754,3213,3672,4131,4590,5049,5508,5967,6426,6885,7344,7803,
Multiples of 465 =465,930,1395,1860,2325,2790,3255,3720,4185,4650,5115,5580,6045,6510,6975,7440,7905,
Now, get the least common multiple of 459, 465 which is 71145
So, the LCM of 459, 465 is 71145.
Least Common Multiple (LCM) of 459 and 465 with the help of Prime Factorisation
One method for determining the LCM of 459 and 465 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 459's prime factorization:
| 3 | 459 |
| 3 | 153 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 459 are 3,17.
459 = 33×171
And this is 465's prime factorization:
| 3 | 465 |
| 5 | 155 |
| 31 | 31 |
| 1 |
Prime factors of 465 are 3, 5,31.
465 = 31×51×311
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: 3,17, 5,31
.33×51×171×311 = 71145
This shows that the LCM of 459 and 465 is 71145.
How to Calculate the LCM of 459 and 465 Using Common Multiples
The first step in determining the Least Common Multiple of 459 and 465 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 459 and 465:
Lets look at the first ten multiples of these numbers, 459 and 465:
459,918,1377,1836,2295,2754,3213,3672,4131,7803 are the first ten multiples of 459.
465,930,1395,1860,2325,2790,3255,3720,4185,7905 are the first ten multiples of 465.
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 459 and 465, for example, are 5508, 7803, and 7440. 71145 is the least common multiple since it is the smallest.
459 and 465 have an LCM of 71145.
Least Common Multiple of 459 and 465 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 459 and 465, than apply into the LCM equation.
GCF(459,465) = 3
LCM(459,465) = ( 459 × 465) / 3
LCM(459,465) = 213435 / 3
LCM(459,465) = 71145
Related Least Common Multiples of 459
Related Least Common Multiples of 465
Frequently Asked Questions on LCM of 459 and 465
1. What is the LCM of 459 and 465?
The LCM of 459 and 465 is 71145.
2. How to find the lowest common multiple of 459 and 465?
To find the lowest common multiple of 459 and 465, we have to get the multip;es of both numbers and identify the least common multiple in them which is 71145.
3. What are the Factors of 459?
Answer: Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459. There are 8 integers that are factors of 459. The greatest factor of 459 is 459.
4. What are the Factors of 465?
Answer: Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. There are 8 integers that are factors of 465. The greatest factor of 465 is 465.
5. How to Find the LCM of 459 and 465?Answer:
Least Common Multiple of 459 and 465 = 71145
Step 1: Find the prime factorization of 459
459 = 3 x 3 x 3 x 17
Step 2: Find the prime factorization of 465
465 = 3 x 5 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 = 71145 = 3 x 3 x 3 x 5 x 17 x 31
Step 4: Therefore, the least common multiple of 459 and 465 is 71145.