LCM of 54 and 58
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 54 and 58 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1566 as output. Here you can check the answer for Find the LCM of 54 and 58.
What is LCM of 54 and 58
Given Numbers are 54, 58
We can find the LCM of 54, 58 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 54 and 58
Multiples of 54 =54,108,162,216,270,324,378,432,486,540,594,648,702,756,810,864,918,
Multiples of 58 =58,116,174,232,290,348,406,464,522,580,638,696,754,812,870,928,986,
Now, get the least common multiple of 54, 58 which is 1566
So, the LCM of 54, 58 is 1566.
Least Common Multiple (LCM) of 54 and 58 with the help of Prime Factorisation
One method for determining the LCM of 54 and 58 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 58's prime factorization:
| 2 | 58 |
| 29 | 29 |
| 1 |
Prime factors of 58 are 2,29.
58 = 21×291
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: 2,3,29
.21×33×291 = 1566
This shows that the LCM of 54 and 58 is 1566.
How to Calculate the LCM of 54 and 58 Using Common Multiples
The first step in determining the Least Common Multiple of 54 and 58 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 54 and 58:
Lets look at the first ten multiples of these numbers, 54 and 58:
54,108,162,216,270,324,378,432,486,918 are the first ten multiples of 54.
58,116,174,232,290,348,406,464,522,986 are the first ten multiples of 58.
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 58, for example, are 648, 918, and 928. 1566 is the least common multiple since it is the smallest.
54 and 58 have an LCM of 1566.
Least Common Multiple of 54 and 58 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 58, than apply into the LCM equation.
GCF(54,58) = 2
LCM(54,58) = ( 54 × 58) / 2
LCM(54,58) = 3132 / 2
LCM(54,58) = 1566
Related Least Common Multiples of 54
Related Least Common Multiples of 58
Frequently Asked Questions on LCM of 54 and 58
1. What is the LCM of 54 and 58?
The LCM of 54 and 58 is 1566.
2. How to find the lowest common multiple of 54 and 58?
To find the lowest common multiple of 54 and 58, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1566.
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 58?
Answer: Factors of 58 are 1, 2, 29, 58. There are 4 integers that are factors of 58. The greatest factor of 58 is 58.
5. How to Find the LCM of 54 and 58?Answer:
Least Common Multiple of 54 and 58 = 1566
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 58
58 = 2 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1566 = 2 x 3 x 3 x 3 x 29
Step 4: Therefore, the least common multiple of 54 and 58 is 1566.