LCM of 96 and 100
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 96 and 100 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2400 as output. Here you can check the answer for Find the LCM of 96 and 100.
What is LCM of 96 and 100
Given Numbers are 96, 100
We can find the LCM of 96, 100 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 96 and 100
Multiples of 96 =96,192,288,384,480,576,672,768,864,960,1056,1152,1248,1344,1440,1536,1632,
Multiples of 100 =100,200,300,400,500,600,700,800,900,1000,1100,1200,1300,1400,1500,1600,1700,
Now, get the least common multiple of 96, 100 which is 2400
So, the LCM of 96, 100 is 2400.
Least Common Multiple (LCM) of 96 and 100 with the help of Prime Factorisation
One method for determining the LCM of 96 and 100 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 96's prime factorization:
| 2 | 96 |
| 2 | 48 |
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 96 are 2,3.
96 = 25×31
And this is 100's prime factorization:
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 100 are 2,5.
100 = 22×52
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
.25×31×52 = 2400
This shows that the LCM of 96 and 100 is 2400.
How to Calculate the LCM of 96 and 100 Using Common Multiples
The first step in determining the Least Common Multiple of 96 and 100 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 96 and 100:
Lets look at the first ten multiples of these numbers, 96 and 100:
96,192,288,384,480,576,672,768,864,1632 are the first ten multiples of 96.
100,200,300,400,500,600,700,800,900,1700 are the first ten multiples of 100.
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 96 and 100, for example, are 1152, 1632, and 1600. 2400 is the least common multiple since it is the smallest.
96 and 100 have an LCM of 2400.
Least Common Multiple of 96 and 100 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96 and 100, than apply into the LCM equation.
GCF(96,100) = 4
LCM(96,100) = ( 96 × 100) / 4
LCM(96,100) = 9600 / 4
LCM(96,100) = 2400
Related Least Common Multiples of 96
Related Least Common Multiples of 100
Frequently Asked Questions on LCM of 96 and 100
1. What is the LCM of 96 and 100?
The LCM of 96 and 100 is 2400.
2. How to find the lowest common multiple of 96 and 100?
To find the lowest common multiple of 96 and 100, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2400.
3. What are the Factors of 96?
Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.
4. What are the Factors of 100?
Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.
5. How to Find the LCM of 96 and 100?Answer:
Least Common Multiple of 96 and 100 = 2400
Step 1: Find the prime factorization of 96
96 = 2 x 2 x 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 100
100 = 2 x 2 x 5 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 = 2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 96 and 100 is 2400.