LCM of 378 and 382
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 378 and 382 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 72198 as output. Here you can check the answer for Find the LCM of 378 and 382.
What is LCM of 378 and 382
Given Numbers are 378, 382
We can find the LCM of 378, 382 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 378 and 382
Multiples of 378 =378,756,1134,1512,1890,2268,2646,3024,3402,3780,4158,4536,4914,5292,5670,6048,6426,
Multiples of 382 =382,764,1146,1528,1910,2292,2674,3056,3438,3820,4202,4584,4966,5348,5730,6112,6494,
Now, get the least common multiple of 378, 382 which is 72198
So, the LCM of 378, 382 is 72198.
Least Common Multiple (LCM) of 378 and 382 with the help of Prime Factorisation
One method for determining the LCM of 378 and 382 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 378's prime factorization:
| 2 | 378 |
| 3 | 189 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 378 are 2, 3,7.
378 = 21×33×71
And this is 382's prime factorization:
| 2 | 382 |
| 191 | 191 |
| 1 |
Prime factors of 382 are 2,191.
382 = 21×1911
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, 3,7,191
.21×33×71×1911 = 72198
This shows that the LCM of 378 and 382 is 72198.
How to Calculate the LCM of 378 and 382 Using Common Multiples
The first step in determining the Least Common Multiple of 378 and 382 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 378 and 382:
Lets look at the first ten multiples of these numbers, 378 and 382:
378,756,1134,1512,1890,2268,2646,3024,3402,6426 are the first ten multiples of 378.
382,764,1146,1528,1910,2292,2674,3056,3438,6494 are the first ten multiples of 382.
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 378 and 382, for example, are 4536, 6426, and 6112. 72198 is the least common multiple since it is the smallest.
378 and 382 have an LCM of 72198.
Least Common Multiple of 378 and 382 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 378 and 382, than apply into the LCM equation.
GCF(378,382) = 2
LCM(378,382) = ( 378 × 382) / 2
LCM(378,382) = 144396 / 2
LCM(378,382) = 72198
Related Least Common Multiples of 378
Related Least Common Multiples of 382
Frequently Asked Questions on LCM of 378 and 382
1. What is the LCM of 378 and 382?
The LCM of 378 and 382 is 72198.
2. How to find the lowest common multiple of 378 and 382?
To find the lowest common multiple of 378 and 382, we have to get the multip;es of both numbers and identify the least common multiple in them which is 72198.
3. What are the Factors of 378?
Answer: Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378. There are 16 integers that are factors of 378. The greatest factor of 378 is 378.
4. What are the Factors of 382?
Answer: Factors of 382 are 1, 2, 191, 382. There are 4 integers that are factors of 382. The greatest factor of 382 is 382.
5. How to Find the LCM of 378 and 382?Answer:
Least Common Multiple of 378 and 382 = 72198
Step 1: Find the prime factorization of 378
378 = 2 x 3 x 3 x 3 x 7
Step 2: Find the prime factorization of 382
382 = 2 x 191
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 72198 = 2 x 3 x 3 x 3 x 7 x 191
Step 4: Therefore, the least common multiple of 378 and 382 is 72198.