LCM of 96 and 102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 96 and 102 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1632 as output. Here you can check the answer for Find the LCM of 96 and 102.
What is LCM of 96 and 102
Given Numbers are 96, 102
We can find the LCM of 96, 102 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 96 and 102
Multiples of 96 =96,192,288,384,480,576,672,768,864,960,1056,1152,1248,1344,1440,1536,1632,
Multiples of 102 =102,204,306,408,510,612,714,816,918,1020,1122,1224,1326,1428,1530,1632,1734,
Now, get the least common multiple of 96, 102 which is 1632
So, the LCM of 96, 102 is 1632.
Least Common Multiple (LCM) of 96 and 102 with the help of Prime Factorisation
One method for determining the LCM of 96 and 102 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 102's prime factorization:
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 102 are 2, 3,17.
102 = 21×31×171
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: 2,3,17
.25×31×171 = 1632
This shows that the LCM of 96 and 102 is 1632.
How to Calculate the LCM of 96 and 102 Using Common Multiples
The first step in determining the Least Common Multiple of 96 and 102 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 96 and 102:
Lets look at the first ten multiples of these numbers, 96 and 102:
96,192,288,384,480,576,672,768,864,1632 are the first ten multiples of 96.
102,204,306,408,510,612,714,816,918,1734 are the first ten multiples of 102.
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 102, for example, are 1152, 1632, and 1632. 1632 is the least common multiple since it is the smallest.
96 and 102 have an LCM of 1632.
Least Common Multiple of 96 and 102 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 102, than apply into the LCM equation.
GCF(96,102) = 6
LCM(96,102) = ( 96 × 102) / 6
LCM(96,102) = 9792 / 6
LCM(96,102) = 1632
Related Least Common Multiples of 96
Related Least Common Multiples of 102
Frequently Asked Questions on LCM of 96 and 102
1. What is the LCM of 96 and 102?
The LCM of 96 and 102 is 1632.
2. How to find the lowest common multiple of 96 and 102?
To find the lowest common multiple of 96 and 102, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1632.
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 102?
Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.
5. How to Find the LCM of 96 and 102?Answer:
Least Common Multiple of 96 and 102 = 1632
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 102
102 = 2 x 3 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1632 = 2 x 2 x 2 x 2 x 2 x 3 x 17
Step 4: Therefore, the least common multiple of 96 and 102 is 1632.