LCM of 460 and 465
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 460 and 465 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 42780 as output. Here you can check the answer for Find the LCM of 460 and 465.
What is LCM of 460 and 465
Given Numbers are 460, 465
We can find the LCM of 460, 465 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 460 and 465
Multiples of 460 =460,920,1380,1840,2300,2760,3220,3680,4140,4600,5060,5520,5980,6440,6900,7360,7820,
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 460, 465 which is 42780
So, the LCM of 460, 465 is 42780.
Least Common Multiple (LCM) of 460 and 465 with the help of Prime Factorisation
One method for determining the LCM of 460 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 460's prime factorization:
| 2 | 460 |
| 2 | 230 |
| 5 | 115 |
| 23 | 23 |
| 1 |
Prime factors of 460 are 2, 5,23.
460 = 22×51×231
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: 2, 5,23, 3,31
.22×31×51×231×311 = 42780
This shows that the LCM of 460 and 465 is 42780.
How to Calculate the LCM of 460 and 465 Using Common Multiples
The first step in determining the Least Common Multiple of 460 and 465 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 460 and 465:
Lets look at the first ten multiples of these numbers, 460 and 465:
460,920,1380,1840,2300,2760,3220,3680,4140,7820 are the first ten multiples of 460.
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 460 and 465, for example, are 5520, 7820, and 7440. 42780 is the least common multiple since it is the smallest.
460 and 465 have an LCM of 42780.
Least Common Multiple of 460 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 460 and 465, than apply into the LCM equation.
GCF(460,465) = 5
LCM(460,465) = ( 460 × 465) / 5
LCM(460,465) = 213900 / 5
LCM(460,465) = 42780
Related Least Common Multiples of 460
Related Least Common Multiples of 465
Frequently Asked Questions on LCM of 460 and 465
1. What is the LCM of 460 and 465?
The LCM of 460 and 465 is 42780.
2. How to find the lowest common multiple of 460 and 465?
To find the lowest common multiple of 460 and 465, we have to get the multip;es of both numbers and identify the least common multiple in them which is 42780.
3. What are the Factors of 460?
Answer: Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. There are 12 integers that are factors of 460. The greatest factor of 460 is 460.
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 460 and 465?Answer:
Least Common Multiple of 460 and 465 = 42780
Step 1: Find the prime factorization of 460
460 = 2 x 2 x 5 x 23
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 = 42780 = 2 x 2 x 3 x 5 x 23 x 31
Step 4: Therefore, the least common multiple of 460 and 465 is 42780.