LCM of 40 and 48
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 40 and 48 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 240 as output. Here you can check the answer for Find the LCM of 40 and 48.
What is LCM of 40 and 48
Given Numbers are 40, 48
We can find the LCM of 40, 48 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 40 and 48
Multiples of 40 =40,80,120,160,200,240,280,320,360,400,440,480,520,560,600,640,680,
Multiples of 48 =48,96,144,192,240,288,336,384,432,480,528,576,624,672,720,768,816,
Now, get the least common multiple of 40, 48 which is 240
So, the LCM of 40, 48 is 240.
Least Common Multiple (LCM) of 40 and 48 with the help of Prime Factorisation
One method for determining the LCM of 40 and 48 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 40's prime factorization:
| 2 | 40 |
| 2 | 20 |
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 40 are 2,5.
40 = 23×51
And this is 48's prime factorization:
| 2 | 48 |
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 48 are 2,3.
48 = 24×31
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: 2,5,3
.24×31×51 = 240
This shows that the LCM of 40 and 48 is 240.
How to Calculate the LCM of 40 and 48 Using Common Multiples
The first step in determining the Least Common Multiple of 40 and 48 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 40 and 48:
Lets look at the first ten multiples of these numbers, 40 and 48:
40,80,120,160,200,240,280,320,360,680 are the first ten multiples of 40.
48,96,144,192,240,288,336,384,432,816 are the first ten multiples of 48.
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 40 and 48, for example, are 480, 680, and 768. 240 is the least common multiple since it is the smallest.
40 and 48 have an LCM of 240.
Least Common Multiple of 40 and 48 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 48, than apply into the LCM equation.
GCF(40,48) = 8
LCM(40,48) = ( 40 × 48) / 8
LCM(40,48) = 1920 / 8
LCM(40,48) = 240
Related Least Common Multiples of 40
Related Least Common Multiples of 48
Frequently Asked Questions on LCM of 40 and 48
1. What is the LCM of 40 and 48?
The LCM of 40 and 48 is 240.
2. How to find the lowest common multiple of 40 and 48?
To find the lowest common multiple of 40 and 48, we have to get the multip;es of both numbers and identify the least common multiple in them which is 240.
3. What are the Factors of 40?
Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.
4. What are the Factors of 48?
Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.
5. How to Find the LCM of 40 and 48?Answer:
Least Common Multiple of 40 and 48 = 240
Step 1: Find the prime factorization of 40
40 = 2 x 2 x 2 x 5
Step 2: Find the prime factorization of 48
48 = 2 x 2 x 2 x 2 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 = 240 = 2 x 2 x 2 x 2 x 3 x 5
Step 4: Therefore, the least common multiple of 40 and 48 is 240.