LCM of 54 and 60
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 54 and 60 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 540 as output. Here you can check the answer for Find the LCM of 54 and 60.
What is LCM of 54 and 60
Given Numbers are 54, 60
We can find the LCM of 54, 60 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 54 and 60
Multiples of 54 =54,108,162,216,270,324,378,432,486,540,594,648,702,756,810,864,918,
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 54, 60 which is 540
So, the LCM of 54, 60 is 540.
Least Common Multiple (LCM) of 54 and 60 with the help of Prime Factorisation
One method for determining the LCM of 54 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 54's prime factorization:
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 54 are 2,3.
54 = 21×33
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: 2,3,5
.22×33×51 = 540
This shows that the LCM of 54 and 60 is 540.
How to Calculate the LCM of 54 and 60 Using Common Multiples
The first step in determining the Least Common Multiple of 54 and 60 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 54 and 60:
Lets look at the first ten multiples of these numbers, 54 and 60:
54,108,162,216,270,324,378,432,486,918 are the first ten multiples of 54.
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 54 and 60, for example, are 648, 918, and 960. 540 is the least common multiple since it is the smallest.
54 and 60 have an LCM of 540.
Least Common Multiple of 54 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 54 and 60, than apply into the LCM equation.
GCF(54,60) = 6
LCM(54,60) = ( 54 × 60) / 6
LCM(54,60) = 3240 / 6
LCM(54,60) = 540
Related Least Common Multiples of 54
Related Least Common Multiples of 60
Frequently Asked Questions on LCM of 54 and 60
1. What is the LCM of 54 and 60?
The LCM of 54 and 60 is 540.
2. How to find the lowest common multiple of 54 and 60?
To find the lowest common multiple of 54 and 60, we have to get the multip;es of both numbers and identify the least common multiple in them which is 540.
3. What are the Factors of 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
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 54 and 60?Answer:
Least Common Multiple of 54 and 60 = 540
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
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 = 540 = 2 x 2 x 3 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 54 and 60 is 540.