LCM of 78 and 82
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 78 and 82 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3198 as output. Here you can check the answer for Find the LCM of 78 and 82.
What is LCM of 78 and 82
Given Numbers are 78, 82
We can find the LCM of 78, 82 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 78 and 82
Multiples of 78 =78,156,234,312,390,468,546,624,702,780,858,936,1014,1092,1170,1248,1326,
Multiples of 82 =82,164,246,328,410,492,574,656,738,820,902,984,1066,1148,1230,1312,1394,
Now, get the least common multiple of 78, 82 which is 3198
So, the LCM of 78, 82 is 3198.
Least Common Multiple (LCM) of 78 and 82 with the help of Prime Factorisation
One method for determining the LCM of 78 and 82 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 78's prime factorization:
| 2 | 78 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 78 are 2, 3,13.
78 = 21×31×131
And this is 82's prime factorization:
| 2 | 82 |
| 41 | 41 |
| 1 |
Prime factors of 82 are 2,41.
82 = 21×411
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, 3,13,41
.21×31×131×411 = 3198
This shows that the LCM of 78 and 82 is 3198.
How to Calculate the LCM of 78 and 82 Using Common Multiples
The first step in determining the Least Common Multiple of 78 and 82 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 78 and 82:
Lets look at the first ten multiples of these numbers, 78 and 82:
78,156,234,312,390,468,546,624,702,1326 are the first ten multiples of 78.
82,164,246,328,410,492,574,656,738,1394 are the first ten multiples of 82.
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 78 and 82, for example, are 936, 1326, and 1312. 3198 is the least common multiple since it is the smallest.
78 and 82 have an LCM of 3198.
Least Common Multiple of 78 and 82 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78 and 82, than apply into the LCM equation.
GCF(78,82) = 2
LCM(78,82) = ( 78 × 82) / 2
LCM(78,82) = 6396 / 2
LCM(78,82) = 3198
Related Least Common Multiples of 78
Related Least Common Multiples of 82
Frequently Asked Questions on LCM of 78 and 82
1. What is the LCM of 78 and 82?
The LCM of 78 and 82 is 3198.
2. How to find the lowest common multiple of 78 and 82?
To find the lowest common multiple of 78 and 82, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3198.
3. What are the Factors of 78?
Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.
4. What are the Factors of 82?
Answer: Factors of 82 are 1, 2, 41, 82. There are 4 integers that are factors of 82. The greatest factor of 82 is 82.
5. How to Find the LCM of 78 and 82?Answer:
Least Common Multiple of 78 and 82 = 3198
Step 1: Find the prime factorization of 78
78 = 2 x 3 x 13
Step 2: Find the prime factorization of 82
82 = 2 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3198 = 2 x 3 x 13 x 41
Step 4: Therefore, the least common multiple of 78 and 82 is 3198.