LCM of 234 and 240
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 234 and 240 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 9360 as output. Here you can check the answer for Find the LCM of 234 and 240.
What is LCM of 234 and 240
Given Numbers are 234, 240
We can find the LCM of 234, 240 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 234 and 240
Multiples of 234 =234,468,702,936,1170,1404,1638,1872,2106,2340,2574,2808,3042,3276,3510,3744,3978,
Multiples of 240 =240,480,720,960,1200,1440,1680,1920,2160,2400,2640,2880,3120,3360,3600,3840,4080,
Now, get the least common multiple of 234, 240 which is 9360
So, the LCM of 234, 240 is 9360.
Least Common Multiple (LCM) of 234 and 240 with the help of Prime Factorisation
One method for determining the LCM of 234 and 240 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 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
And this is 240's prime factorization:
| 2 | 240 |
| 2 | 120 |
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 240 are 2, 3,5.
240 = 24×31×51
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, 3,13,5
.24×32×51×131 = 9360
This shows that the LCM of 234 and 240 is 9360.
How to Calculate the LCM of 234 and 240 Using Common Multiples
The first step in determining the Least Common Multiple of 234 and 240 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 234 and 240:
Lets look at the first ten multiples of these numbers, 234 and 240:
234,468,702,936,1170,1404,1638,1872,2106,3978 are the first ten multiples of 234.
240,480,720,960,1200,1440,1680,1920,2160,4080 are the first ten multiples of 240.
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 234 and 240, for example, are 2808, 3978, and 3840. 9360 is the least common multiple since it is the smallest.
234 and 240 have an LCM of 9360.
Least Common Multiple of 234 and 240 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 234 and 240, than apply into the LCM equation.
GCF(234,240) = 6
LCM(234,240) = ( 234 × 240) / 6
LCM(234,240) = 56160 / 6
LCM(234,240) = 9360
Related Least Common Multiples of 234
Related Least Common Multiples of 240
Frequently Asked Questions on LCM of 234 and 240
1. What is the LCM of 234 and 240?
The LCM of 234 and 240 is 9360.
2. How to find the lowest common multiple of 234 and 240?
To find the lowest common multiple of 234 and 240, we have to get the multip;es of both numbers and identify the least common multiple in them which is 9360.
3. 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.
4. What are the Factors of 240?
Answer: Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. There are 20 integers that are factors of 240. The greatest factor of 240 is 240.
5. How to Find the LCM of 234 and 240?Answer:
Least Common Multiple of 234 and 240 = 9360
Step 1: Find the prime factorization of 234
234 = 2 x 3 x 3 x 13
Step 2: Find the prime factorization of 240
240 = 2 x 2 x 2 x 2 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9360 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 234 and 240 is 9360.