LCM of 54 and 61
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 54 and 61 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3294 as output. Here you can check the answer for Find the LCM of 54 and 61.
What is LCM of 54 and 61
Given Numbers are 54, 61
We can find the LCM of 54, 61 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 54 and 61
Multiples of 54 =54,108,162,216,270,324,378,432,486,540,594,648,702,756,810,864,918,
Multiples of 61 =61,122,183,244,305,366,427,488,549,610,671,732,793,854,915,976,1037,
Now, get the least common multiple of 54, 61 which is 3294
So, the LCM of 54, 61 is 3294.
Least Common Multiple (LCM) of 54 and 61 with the help of Prime Factorisation
One method for determining the LCM of 54 and 61 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 61's prime factorization:
| 61 | 61 |
| 1 |
Prime factors of 61 are 61.
61 = 611
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: 2,3,61
.21×33×611 = 3294
This shows that the LCM of 54 and 61 is 3294.
How to Calculate the LCM of 54 and 61 Using Common Multiples
The first step in determining the Least Common Multiple of 54 and 61 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 54 and 61:
Lets look at the first ten multiples of these numbers, 54 and 61:
54,108,162,216,270,324,378,432,486,918 are the first ten multiples of 54.
61,122,183,244,305,366,427,488,549,1037 are the first ten multiples of 61.
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 61, for example, are 648, 918, and 976. 3294 is the least common multiple since it is the smallest.
54 and 61 have an LCM of 3294.
Least Common Multiple of 54 and 61 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 61, than apply into the LCM equation.
GCF(54,61) = 1
LCM(54,61) = ( 54 × 61) / 1
LCM(54,61) = 3294 / 1
LCM(54,61) = 3294
Related Least Common Multiples of 54
Related Least Common Multiples of 61
Frequently Asked Questions on LCM of 54 and 61
1. What is the LCM of 54 and 61?
The LCM of 54 and 61 is 3294.
2. How to find the lowest common multiple of 54 and 61?
To find the lowest common multiple of 54 and 61, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3294.
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 61?
Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.
5. How to Find the LCM of 54 and 61?Answer:
Least Common Multiple of 54 and 61 = 3294
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 61
61 = 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3294 = 2 x 3 x 3 x 3 x 61
Step 4: Therefore, the least common multiple of 54 and 61 is 3294.