LCM of 240 and 245
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 240 and 245 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 11760 as output. Here you can check the answer for Find the LCM of 240 and 245.
What is LCM of 240 and 245
Given Numbers are 240, 245
We can find the LCM of 240, 245 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 240 and 245
Multiples of 240 =240,480,720,960,1200,1440,1680,1920,2160,2400,2640,2880,3120,3360,3600,3840,4080,
Multiples of 245 =245,490,735,980,1225,1470,1715,1960,2205,2450,2695,2940,3185,3430,3675,3920,4165,
Now, get the least common multiple of 240, 245 which is 11760
So, the LCM of 240, 245 is 11760.
Least Common Multiple (LCM) of 240 and 245 with the help of Prime Factorisation
One method for determining the LCM of 240 and 245 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 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
And this is 245's prime factorization:
| 5 | 245 |
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 245 are 5,7.
245 = 51×72
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, 3,5,7
.24×31×51×72 = 11760
This shows that the LCM of 240 and 245 is 11760.
How to Calculate the LCM of 240 and 245 Using Common Multiples
The first step in determining the Least Common Multiple of 240 and 245 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 240 and 245:
Lets look at the first ten multiples of these numbers, 240 and 245:
240,480,720,960,1200,1440,1680,1920,2160,4080 are the first ten multiples of 240.
245,490,735,980,1225,1470,1715,1960,2205,4165 are the first ten multiples of 245.
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 240 and 245, for example, are 2880, 4080, and 3920. 11760 is the least common multiple since it is the smallest.
240 and 245 have an LCM of 11760.
Least Common Multiple of 240 and 245 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 240 and 245, than apply into the LCM equation.
GCF(240,245) = 5
LCM(240,245) = ( 240 × 245) / 5
LCM(240,245) = 58800 / 5
LCM(240,245) = 11760
Related Least Common Multiples of 240
Related Least Common Multiples of 245
Frequently Asked Questions on LCM of 240 and 245
1. What is the LCM of 240 and 245?
The LCM of 240 and 245 is 11760.
2. How to find the lowest common multiple of 240 and 245?
To find the lowest common multiple of 240 and 245, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11760.
3. 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.
4. What are the Factors of 245?
Answer: Factors of 245 are 1, 5, 7, 35, 49, 245. There are 6 integers that are factors of 245. The greatest factor of 245 is 245.
5. How to Find the LCM of 240 and 245?Answer:
Least Common Multiple of 240 and 245 = 11760
Step 1: Find the prime factorization of 240
240 = 2 x 2 x 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 245
245 = 5 x 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11760 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7
Step 4: Therefore, the least common multiple of 240 and 245 is 11760.