LCM of 228 and 234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 228 and 234 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 8892 as output. Here you can check the answer for Find the LCM of 228 and 234.
What is LCM of 228 and 234
Given Numbers are 228, 234
We can find the LCM of 228, 234 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 228 and 234
Multiples of 228 =228,456,684,912,1140,1368,1596,1824,2052,2280,2508,2736,2964,3192,3420,3648,3876,
Multiples of 234 =234,468,702,936,1170,1404,1638,1872,2106,2340,2574,2808,3042,3276,3510,3744,3978,
Now, get the least common multiple of 228, 234 which is 8892
So, the LCM of 228, 234 is 8892.
Least Common Multiple (LCM) of 228 and 234 with the help of Prime Factorisation
One method for determining the LCM of 228 and 234 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 228's prime factorization:
| 2 | 228 |
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 228 are 2, 3,19.
228 = 22×31×191
And this is 234's prime factorization:
| 2 | 234 |
| 3 | 117 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 234 are 2, 3,13.
234 = 21×32×131
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, 3,19,13
.22×32×131×191 = 8892
This shows that the LCM of 228 and 234 is 8892.
How to Calculate the LCM of 228 and 234 Using Common Multiples
The first step in determining the Least Common Multiple of 228 and 234 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 228 and 234:
Lets look at the first ten multiples of these numbers, 228 and 234:
228,456,684,912,1140,1368,1596,1824,2052,3876 are the first ten multiples of 228.
234,468,702,936,1170,1404,1638,1872,2106,3978 are the first ten multiples of 234.
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 228 and 234, for example, are 2736, 3876, and 3744. 8892 is the least common multiple since it is the smallest.
228 and 234 have an LCM of 8892.
Least Common Multiple of 228 and 234 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 228 and 234, than apply into the LCM equation.
GCF(228,234) = 6
LCM(228,234) = ( 228 × 234) / 6
LCM(228,234) = 53352 / 6
LCM(228,234) = 8892
Related Least Common Multiples of 228
Related Least Common Multiples of 234
Frequently Asked Questions on LCM of 228 and 234
1. What is the LCM of 228 and 234?
The LCM of 228 and 234 is 8892.
2. How to find the lowest common multiple of 228 and 234?
To find the lowest common multiple of 228 and 234, we have to get the multip;es of both numbers and identify the least common multiple in them which is 8892.
3. What are the Factors of 228?
Answer: Factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228. There are 12 integers that are factors of 228. The greatest factor of 228 is 228.
4. What are the Factors of 234?
Answer: Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234. There are 12 integers that are factors of 234. The greatest factor of 234 is 234.
5. How to Find the LCM of 228 and 234?Answer:
Least Common Multiple of 228 and 234 = 8892
Step 1: Find the prime factorization of 228
228 = 2 x 2 x 3 x 19
Step 2: Find the prime factorization of 234
234 = 2 x 3 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8892 = 2 x 2 x 3 x 3 x 13 x 19
Step 4: Therefore, the least common multiple of 228 and 234 is 8892.