LCM of 228 and 232
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 228 and 232 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 13224 as output. Here you can check the answer for Find the LCM of 228 and 232.
What is LCM of 228 and 232
Given Numbers are 228, 232
We can find the LCM of 228, 232 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 228 and 232
Multiples of 228 =228,456,684,912,1140,1368,1596,1824,2052,2280,2508,2736,2964,3192,3420,3648,3876,
Multiples of 232 =232,464,696,928,1160,1392,1624,1856,2088,2320,2552,2784,3016,3248,3480,3712,3944,
Now, get the least common multiple of 228, 232 which is 13224
So, the LCM of 228, 232 is 13224.
Least Common Multiple (LCM) of 228 and 232 with the help of Prime Factorisation
One method for determining the LCM of 228 and 232 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 232's prime factorization:
| 2 | 232 |
| 2 | 116 |
| 2 | 58 |
| 29 | 29 |
| 1 |
Prime factors of 232 are 2,29.
232 = 23×291
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, 3,19,29
.23×31×191×291 = 13224
This shows that the LCM of 228 and 232 is 13224.
How to Calculate the LCM of 228 and 232 Using Common Multiples
The first step in determining the Least Common Multiple of 228 and 232 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 228 and 232:
Lets look at the first ten multiples of these numbers, 228 and 232:
228,456,684,912,1140,1368,1596,1824,2052,3876 are the first ten multiples of 228.
232,464,696,928,1160,1392,1624,1856,2088,3944 are the first ten multiples of 232.
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 232, for example, are 2736, 3876, and 3712. 13224 is the least common multiple since it is the smallest.
228 and 232 have an LCM of 13224.
Least Common Multiple of 228 and 232 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 232, than apply into the LCM equation.
GCF(228,232) = 4
LCM(228,232) = ( 228 × 232) / 4
LCM(228,232) = 52896 / 4
LCM(228,232) = 13224
Related Least Common Multiples of 228
Related Least Common Multiples of 232
Frequently Asked Questions on LCM of 228 and 232
1. What is the LCM of 228 and 232?
The LCM of 228 and 232 is 13224.
2. How to find the lowest common multiple of 228 and 232?
To find the lowest common multiple of 228 and 232, we have to get the multip;es of both numbers and identify the least common multiple in them which is 13224.
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 232?
Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.
5. How to Find the LCM of 228 and 232?Answer:
Least Common Multiple of 228 and 232 = 13224
Step 1: Find the prime factorization of 228
228 = 2 x 2 x 3 x 19
Step 2: Find the prime factorization of 232
232 = 2 x 2 x 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 = 13224 = 2 x 2 x 2 x 3 x 19 x 29
Step 4: Therefore, the least common multiple of 228 and 232 is 13224.