LCM of 46 and 54
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 46 and 54 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1242 as output. Here you can check the answer for Find the LCM of 46 and 54.
What is LCM of 46 and 54
Given Numbers are 46, 54
We can find the LCM of 46, 54 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 46 and 54
Multiples of 46 =46,92,138,184,230,276,322,368,414,460,506,552,598,644,690,736,782,
Multiples of 54 =54,108,162,216,270,324,378,432,486,540,594,648,702,756,810,864,918,
Now, get the least common multiple of 46, 54 which is 1242
So, the LCM of 46, 54 is 1242.
Least Common Multiple (LCM) of 46 and 54 with the help of Prime Factorisation
One method for determining the LCM of 46 and 54 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 46's prime factorization:
| 2 | 46 |
| 23 | 23 |
| 1 |
Prime factors of 46 are 2,23.
46 = 21×231
And this is 54's prime factorization:
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 54 are 2,3.
54 = 21×33
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: 2,23,3
.21×33×231 = 1242
This shows that the LCM of 46 and 54 is 1242.
How to Calculate the LCM of 46 and 54 Using Common Multiples
The first step in determining the Least Common Multiple of 46 and 54 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 46 and 54:
Lets look at the first ten multiples of these numbers, 46 and 54:
46,92,138,184,230,276,322,368,414,782 are the first ten multiples of 46.
54,108,162,216,270,324,378,432,486,918 are the first ten multiples of 54.
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 46 and 54, for example, are 552, 782, and 864. 1242 is the least common multiple since it is the smallest.
46 and 54 have an LCM of 1242.
Least Common Multiple of 46 and 54 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46 and 54, than apply into the LCM equation.
GCF(46,54) = 2
LCM(46,54) = ( 46 × 54) / 2
LCM(46,54) = 2484 / 2
LCM(46,54) = 1242
Related Least Common Multiples of 46
Related Least Common Multiples of 54
Frequently Asked Questions on LCM of 46 and 54
1. What is the LCM of 46 and 54?
The LCM of 46 and 54 is 1242.
2. How to find the lowest common multiple of 46 and 54?
To find the lowest common multiple of 46 and 54, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1242.
3. What are the Factors of 46?
Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.
4. 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.
5. How to Find the LCM of 46 and 54?Answer:
Least Common Multiple of 46 and 54 = 1242
Step 1: Find the prime factorization of 46
46 = 2 x 23
Step 2: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1242 = 2 x 3 x 3 x 3 x 23
Step 4: Therefore, the least common multiple of 46 and 54 is 1242.