LCM of 60 and 65
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 60 and 65 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 780 as output. Here you can check the answer for Find the LCM of 60 and 65.
What is LCM of 60 and 65
Given Numbers are 60, 65
We can find the LCM of 60, 65 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 60 and 65
Multiples of 60 =60,120,180,240,300,360,420,480,540,600,660,720,780,840,900,960,1020,
Multiples of 65 =65,130,195,260,325,390,455,520,585,650,715,780,845,910,975,1040,1105,
Now, get the least common multiple of 60, 65 which is 780
So, the LCM of 60, 65 is 780.
Least Common Multiple (LCM) of 60 and 65 with the help of Prime Factorisation
One method for determining the LCM of 60 and 65 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 60's prime factorization:
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 60 are 2, 3,5.
60 = 22×31×51
And this is 65's prime factorization:
| 5 | 65 |
| 13 | 13 |
| 1 |
Prime factors of 65 are 5,13.
65 = 51×131
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, 3,5,13
.22×31×51×131 = 780
This shows that the LCM of 60 and 65 is 780.
How to Calculate the LCM of 60 and 65 Using Common Multiples
The first step in determining the Least Common Multiple of 60 and 65 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 60 and 65:
Lets look at the first ten multiples of these numbers, 60 and 65:
60,120,180,240,300,360,420,480,540,1020 are the first ten multiples of 60.
65,130,195,260,325,390,455,520,585,1105 are the first ten multiples of 65.
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 60 and 65, for example, are 720, 1020, and 1040. 780 is the least common multiple since it is the smallest.
60 and 65 have an LCM of 780.
Least Common Multiple of 60 and 65 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 60 and 65, than apply into the LCM equation.
GCF(60,65) = 5
LCM(60,65) = ( 60 × 65) / 5
LCM(60,65) = 3900 / 5
LCM(60,65) = 780
Related Least Common Multiples of 60
Related Least Common Multiples of 65
Frequently Asked Questions on LCM of 60 and 65
1. What is the LCM of 60 and 65?
The LCM of 60 and 65 is 780.
2. How to find the lowest common multiple of 60 and 65?
To find the lowest common multiple of 60 and 65, we have to get the multip;es of both numbers and identify the least common multiple in them which is 780.
3. What are the Factors of 60?
Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.
4. What are the Factors of 65?
Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.
5. How to Find the LCM of 60 and 65?Answer:
Least Common Multiple of 60 and 65 = 780
Step 1: Find the prime factorization of 60
60 = 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 65
65 = 5 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 780 = 2 x 2 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 60 and 65 is 780.