LCM of 240 and 248
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 240 and 248 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 7440 as output. Here you can check the answer for Find the LCM of 240 and 248.
What is LCM of 240 and 248
Given Numbers are 240, 248
We can find the LCM of 240, 248 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 240 and 248
Multiples of 240 =240,480,720,960,1200,1440,1680,1920,2160,2400,2640,2880,3120,3360,3600,3840,4080,
Multiples of 248 =248,496,744,992,1240,1488,1736,1984,2232,2480,2728,2976,3224,3472,3720,3968,4216,
Now, get the least common multiple of 240, 248 which is 7440
So, the LCM of 240, 248 is 7440.
Least Common Multiple (LCM) of 240 and 248 with the help of Prime Factorisation
One method for determining the LCM of 240 and 248 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 248's prime factorization:
| 2 | 248 |
| 2 | 124 |
| 2 | 62 |
| 31 | 31 |
| 1 |
Prime factors of 248 are 2,31.
248 = 23×311
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, 3,5,31
.24×31×51×311 = 7440
This shows that the LCM of 240 and 248 is 7440.
How to Calculate the LCM of 240 and 248 Using Common Multiples
The first step in determining the Least Common Multiple of 240 and 248 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 240 and 248:
Lets look at the first ten multiples of these numbers, 240 and 248:
240,480,720,960,1200,1440,1680,1920,2160,4080 are the first ten multiples of 240.
248,496,744,992,1240,1488,1736,1984,2232,4216 are the first ten multiples of 248.
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 248, for example, are 2880, 4080, and 3968. 7440 is the least common multiple since it is the smallest.
240 and 248 have an LCM of 7440.
Least Common Multiple of 240 and 248 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 248, than apply into the LCM equation.
GCF(240,248) = 8
LCM(240,248) = ( 240 × 248) / 8
LCM(240,248) = 59520 / 8
LCM(240,248) = 7440
Related Least Common Multiples of 240
Related Least Common Multiples of 248
Frequently Asked Questions on LCM of 240 and 248
1. What is the LCM of 240 and 248?
The LCM of 240 and 248 is 7440.
2. How to find the lowest common multiple of 240 and 248?
To find the lowest common multiple of 240 and 248, we have to get the multip;es of both numbers and identify the least common multiple in them which is 7440.
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 248?
Answer: Factors of 248 are 1, 2, 4, 8, 31, 62, 124, 248. There are 8 integers that are factors of 248. The greatest factor of 248 is 248.
5. How to Find the LCM of 240 and 248?Answer:
Least Common Multiple of 240 and 248 = 7440
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 248
248 = 2 x 2 x 2 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7440 = 2 x 2 x 2 x 2 x 3 x 5 x 31
Step 4: Therefore, the least common multiple of 240 and 248 is 7440.