LCM of 360 and 365
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 360 and 365 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 26280 as output. Here you can check the answer for Find the LCM of 360 and 365.
What is LCM of 360 and 365
Given Numbers are 360, 365
We can find the LCM of 360, 365 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 360 and 365
Multiples of 360 =360,720,1080,1440,1800,2160,2520,2880,3240,3600,3960,4320,4680,5040,5400,5760,6120,
Multiples of 365 =365,730,1095,1460,1825,2190,2555,2920,3285,3650,4015,4380,4745,5110,5475,5840,6205,
Now, get the least common multiple of 360, 365 which is 26280
So, the LCM of 360, 365 is 26280.
Least Common Multiple (LCM) of 360 and 365 with the help of Prime Factorisation
One method for determining the LCM of 360 and 365 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 360's prime factorization:
| 2 | 360 |
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 360 are 2, 3,5.
360 = 23×32×51
And this is 365's prime factorization:
| 5 | 365 |
| 73 | 73 |
| 1 |
Prime factors of 365 are 5,73.
365 = 51×731
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, 3,5,73
.23×32×51×731 = 26280
This shows that the LCM of 360 and 365 is 26280.
How to Calculate the LCM of 360 and 365 Using Common Multiples
The first step in determining the Least Common Multiple of 360 and 365 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 360 and 365:
Lets look at the first ten multiples of these numbers, 360 and 365:
360,720,1080,1440,1800,2160,2520,2880,3240,6120 are the first ten multiples of 360.
365,730,1095,1460,1825,2190,2555,2920,3285,6205 are the first ten multiples of 365.
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 360 and 365, for example, are 4320, 6120, and 5840. 26280 is the least common multiple since it is the smallest.
360 and 365 have an LCM of 26280.
Least Common Multiple of 360 and 365 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 360 and 365, than apply into the LCM equation.
GCF(360,365) = 5
LCM(360,365) = ( 360 × 365) / 5
LCM(360,365) = 131400 / 5
LCM(360,365) = 26280
Related Least Common Multiples of 360
Related Least Common Multiples of 365
Frequently Asked Questions on LCM of 360 and 365
1. What is the LCM of 360 and 365?
The LCM of 360 and 365 is 26280.
2. How to find the lowest common multiple of 360 and 365?
To find the lowest common multiple of 360 and 365, we have to get the multip;es of both numbers and identify the least common multiple in them which is 26280.
3. What are the Factors of 360?
Answer: Factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. There are 24 integers that are factors of 360. The greatest factor of 360 is 360.
4. What are the Factors of 365?
Answer: Factors of 365 are 1, 5, 73, 365. There are 4 integers that are factors of 365. The greatest factor of 365 is 365.
5. How to Find the LCM of 360 and 365?Answer:
Least Common Multiple of 360 and 365 = 26280
Step 1: Find the prime factorization of 360
360 = 2 x 2 x 2 x 3 x 3 x 5
Step 2: Find the prime factorization of 365
365 = 5 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 26280 = 2 x 2 x 2 x 3 x 3 x 5 x 73
Step 4: Therefore, the least common multiple of 360 and 365 is 26280.