LCM of 465 and 470
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 465 and 470 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 43710 as output. Here you can check the answer for Find the LCM of 465 and 470.
What is LCM of 465 and 470
Given Numbers are 465, 470
We can find the LCM of 465, 470 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 465 and 470
Multiples of 465 =465,930,1395,1860,2325,2790,3255,3720,4185,4650,5115,5580,6045,6510,6975,7440,7905,
Multiples of 470 =470,940,1410,1880,2350,2820,3290,3760,4230,4700,5170,5640,6110,6580,7050,7520,7990,
Now, get the least common multiple of 465, 470 which is 43710
So, the LCM of 465, 470 is 43710.
Least Common Multiple (LCM) of 465 and 470 with the help of Prime Factorisation
One method for determining the LCM of 465 and 470 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 465's prime factorization:
| 3 | 465 |
| 5 | 155 |
| 31 | 31 |
| 1 |
Prime factors of 465 are 3, 5,31.
465 = 31×51×311
And this is 470's prime factorization:
| 2 | 470 |
| 5 | 235 |
| 47 | 47 |
| 1 |
Prime factors of 470 are 2, 5,47.
470 = 21×51×471
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, 5,31, 2,47
.21×31×51×311×471 = 43710
This shows that the LCM of 465 and 470 is 43710.
How to Calculate the LCM of 465 and 470 Using Common Multiples
The first step in determining the Least Common Multiple of 465 and 470 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 465 and 470:
Lets look at the first ten multiples of these numbers, 465 and 470:
465,930,1395,1860,2325,2790,3255,3720,4185,7905 are the first ten multiples of 465.
470,940,1410,1880,2350,2820,3290,3760,4230,7990 are the first ten multiples of 470.
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 465 and 470, for example, are 5580, 7905, and 7520. 43710 is the least common multiple since it is the smallest.
465 and 470 have an LCM of 43710.
Least Common Multiple of 465 and 470 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 465 and 470, than apply into the LCM equation.
GCF(465,470) = 5
LCM(465,470) = ( 465 × 470) / 5
LCM(465,470) = 218550 / 5
LCM(465,470) = 43710
Related Least Common Multiples of 465
Related Least Common Multiples of 470
Frequently Asked Questions on LCM of 465 and 470
1. What is the LCM of 465 and 470?
The LCM of 465 and 470 is 43710.
2. How to find the lowest common multiple of 465 and 470?
To find the lowest common multiple of 465 and 470, we have to get the multip;es of both numbers and identify the least common multiple in them which is 43710.
3. 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.
4. What are the Factors of 470?
Answer: Factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470. There are 8 integers that are factors of 470. The greatest factor of 470 is 470.
5. How to Find the LCM of 465 and 470?Answer:
Least Common Multiple of 465 and 470 = 43710
Step 1: Find the prime factorization of 465
465 = 3 x 5 x 31
Step 2: Find the prime factorization of 470
470 = 2 x 5 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 43710 = 2 x 3 x 5 x 31 x 47
Step 4: Therefore, the least common multiple of 465 and 470 is 43710.