LCM of 238 and 243
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 238 and 243 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 57834 as output. Here you can check the answer for Find the LCM of 238 and 243.
What is LCM of 238 and 243
Given Numbers are 238, 243
We can find the LCM of 238, 243 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 238 and 243
Multiples of 238 =238,476,714,952,1190,1428,1666,1904,2142,2380,2618,2856,3094,3332,3570,3808,4046,
Multiples of 243 =243,486,729,972,1215,1458,1701,1944,2187,2430,2673,2916,3159,3402,3645,3888,4131,
Now, get the least common multiple of 238, 243 which is 57834
So, the LCM of 238, 243 is 57834.
Least Common Multiple (LCM) of 238 and 243 with the help of Prime Factorisation
One method for determining the LCM of 238 and 243 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 238's prime factorization:
| 2 | 238 |
| 7 | 119 |
| 17 | 17 |
| 1 |
Prime factors of 238 are 2, 7,17.
238 = 21×71×171
And this is 243's prime factorization:
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 243 are 3.
243 = 35
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, 7,17,3
.21×35×71×171 = 57834
This shows that the LCM of 238 and 243 is 57834.
How to Calculate the LCM of 238 and 243 Using Common Multiples
The first step in determining the Least Common Multiple of 238 and 243 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 238 and 243:
Lets look at the first ten multiples of these numbers, 238 and 243:
238,476,714,952,1190,1428,1666,1904,2142,4046 are the first ten multiples of 238.
243,486,729,972,1215,1458,1701,1944,2187,4131 are the first ten multiples of 243.
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 238 and 243, for example, are 2856, 4046, and 3888. 57834 is the least common multiple since it is the smallest.
238 and 243 have an LCM of 57834.
Least Common Multiple of 238 and 243 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 238 and 243, than apply into the LCM equation.
GCF(238,243) = 1
LCM(238,243) = ( 238 × 243) / 1
LCM(238,243) = 57834 / 1
LCM(238,243) = 57834
Related Least Common Multiples of 238
Related Least Common Multiples of 243
Frequently Asked Questions on LCM of 238 and 243
1. What is the LCM of 238 and 243?
The LCM of 238 and 243 is 57834.
2. How to find the lowest common multiple of 238 and 243?
To find the lowest common multiple of 238 and 243, we have to get the multip;es of both numbers and identify the least common multiple in them which is 57834.
3. What are the Factors of 238?
Answer: Factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238. There are 8 integers that are factors of 238. The greatest factor of 238 is 238.
4. What are the Factors of 243?
Answer: Factors of 243 are 1, 3, 9, 27, 81, 243. There are 6 integers that are factors of 243. The greatest factor of 243 is 243.
5. How to Find the LCM of 238 and 243?Answer:
Least Common Multiple of 238 and 243 = 57834
Step 1: Find the prime factorization of 238
238 = 2 x 7 x 17
Step 2: Find the prime factorization of 243
243 = 3 x 3 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 = 57834 = 2 x 3 x 3 x 3 x 3 x 3 x 7 x 17
Step 4: Therefore, the least common multiple of 238 and 243 is 57834.