LCM of 54 and 59
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 54 and 59 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3186 as output. Here you can check the answer for Find the LCM of 54 and 59.
What is LCM of 54 and 59
Given Numbers are 54, 59
We can find the LCM of 54, 59 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 54 and 59
Multiples of 54 =54,108,162,216,270,324,378,432,486,540,594,648,702,756,810,864,918,
Multiples of 59 =59,118,177,236,295,354,413,472,531,590,649,708,767,826,885,944,1003,
Now, get the least common multiple of 54, 59 which is 3186
So, the LCM of 54, 59 is 3186.
Least Common Multiple (LCM) of 54 and 59 with the help of Prime Factorisation
One method for determining the LCM of 54 and 59 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 59's prime factorization:
| 59 | 59 |
| 1 |
Prime factors of 59 are 59.
59 = 591
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: 2,3,59
.21×33×591 = 3186
This shows that the LCM of 54 and 59 is 3186.
How to Calculate the LCM of 54 and 59 Using Common Multiples
The first step in determining the Least Common Multiple of 54 and 59 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 54 and 59:
Lets look at the first ten multiples of these numbers, 54 and 59:
54,108,162,216,270,324,378,432,486,918 are the first ten multiples of 54.
59,118,177,236,295,354,413,472,531,1003 are the first ten multiples of 59.
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 59, for example, are 648, 918, and 944. 3186 is the least common multiple since it is the smallest.
54 and 59 have an LCM of 3186.
Least Common Multiple of 54 and 59 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 59, than apply into the LCM equation.
GCF(54,59) = 1
LCM(54,59) = ( 54 × 59) / 1
LCM(54,59) = 3186 / 1
LCM(54,59) = 3186
Related Least Common Multiples of 54
Related Least Common Multiples of 59
Frequently Asked Questions on LCM of 54 and 59
1. What is the LCM of 54 and 59?
The LCM of 54 and 59 is 3186.
2. How to find the lowest common multiple of 54 and 59?
To find the lowest common multiple of 54 and 59, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3186.
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 59?
Answer: Factors of 59 are 1, 59. There are 2 integers that are factors of 59. The greatest factor of 59 is 59.
5. How to Find the LCM of 54 and 59?Answer:
Least Common Multiple of 54 and 59 = 3186
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 59
59 = 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3186 = 2 x 3 x 3 x 3 x 59
Step 4: Therefore, the least common multiple of 54 and 59 is 3186.