LCM of 65 and 72
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 65 and 72 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4680 as output. Here you can check the answer for Find the LCM of 65 and 72.
What is LCM of 65 and 72
Given Numbers are 65, 72
We can find the LCM of 65, 72 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 65 and 72
Multiples of 65 =65,130,195,260,325,390,455,520,585,650,715,780,845,910,975,1040,1105,
Multiples of 72 =72,144,216,288,360,432,504,576,648,720,792,864,936,1008,1080,1152,1224,
Now, get the least common multiple of 65, 72 which is 4680
So, the LCM of 65, 72 is 4680.
Least Common Multiple (LCM) of 65 and 72 with the help of Prime Factorisation
One method for determining the LCM of 65 and 72 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 65's prime factorization:
| 5 | 65 |
| 13 | 13 |
| 1 |
Prime factors of 65 are 5,13.
65 = 51×131
And this is 72's prime factorization:
| 2 | 72 |
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 72 are 2,3.
72 = 23×32
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: 5,13, 2,3
.23×32×51×131 = 4680
This shows that the LCM of 65 and 72 is 4680.
How to Calculate the LCM of 65 and 72 Using Common Multiples
The first step in determining the Least Common Multiple of 65 and 72 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 65 and 72:
Lets look at the first ten multiples of these numbers, 65 and 72:
65,130,195,260,325,390,455,520,585,1105 are the first ten multiples of 65.
72,144,216,288,360,432,504,576,648,1224 are the first ten multiples of 72.
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 65 and 72, for example, are 780, 1105, and 1152. 4680 is the least common multiple since it is the smallest.
65 and 72 have an LCM of 4680.
Least Common Multiple of 65 and 72 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 72, than apply into the LCM equation.
GCF(65,72) = 1
LCM(65,72) = ( 65 × 72) / 1
LCM(65,72) = 4680 / 1
LCM(65,72) = 4680
Related Least Common Multiples of 65
Related Least Common Multiples of 72
Frequently Asked Questions on LCM of 65 and 72
1. What is the LCM of 65 and 72?
The LCM of 65 and 72 is 4680.
2. How to find the lowest common multiple of 65 and 72?
To find the lowest common multiple of 65 and 72, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4680.
3. 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.
4. What are the Factors of 72?
Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.
5. How to Find the LCM of 65 and 72?Answer:
Least Common Multiple of 65 and 72 = 4680
Step 1: Find the prime factorization of 65
65 = 5 x 13
Step 2: Find the prime factorization of 72
72 = 2 x 2 x 2 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4680 = 2 x 2 x 2 x 3 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 65 and 72 is 4680.