LCM of 52 and 60
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 52 and 60 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 52 and 60.
What is LCM of 52 and 60
Given Numbers are 52, 60
We can find the LCM of 52, 60 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 52 and 60
Multiples of 52 =52,104,156,208,260,312,364,416,468,520,572,624,676,728,780,832,884,
Multiples of 60 =60,120,180,240,300,360,420,480,540,600,660,720,780,840,900,960,1020,
Now, get the least common multiple of 52, 60 which is 780
So, the LCM of 52, 60 is 780.
Least Common Multiple (LCM) of 52 and 60 with the help of Prime Factorisation
One method for determining the LCM of 52 and 60 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 52's prime factorization:
| 2 | 52 |
| 2 | 26 |
| 13 | 13 |
| 1 |
Prime factors of 52 are 2,13.
52 = 22×131
And this 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
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: 2,13, 3,5
.22×31×51×131 = 780
This shows that the LCM of 52 and 60 is 780.
How to Calculate the LCM of 52 and 60 Using Common Multiples
The first step in determining the Least Common Multiple of 52 and 60 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 52 and 60:
Lets look at the first ten multiples of these numbers, 52 and 60:
52,104,156,208,260,312,364,416,468,884 are the first ten multiples of 52.
60,120,180,240,300,360,420,480,540,1020 are the first ten multiples of 60.
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 52 and 60, for example, are 624, 884, and 960. 780 is the least common multiple since it is the smallest.
52 and 60 have an LCM of 780.
Least Common Multiple of 52 and 60 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 52 and 60, than apply into the LCM equation.
GCF(52,60) = 4
LCM(52,60) = ( 52 × 60) / 4
LCM(52,60) = 3120 / 4
LCM(52,60) = 780
Related Least Common Multiples of 52
Related Least Common Multiples of 60
Frequently Asked Questions on LCM of 52 and 60
1. What is the LCM of 52 and 60?
The LCM of 52 and 60 is 780.
2. How to find the lowest common multiple of 52 and 60?
To find the lowest common multiple of 52 and 60, 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 52?
Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.
4. 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.
5. How to Find the LCM of 52 and 60?Answer:
Least Common Multiple of 52 and 60 = 780
Step 1: Find the prime factorization of 52
52 = 2 x 2 x 13
Step 2: Find the prime factorization of 60
60 = 2 x 2 x 3 x 5
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 52 and 60 is 780.