LCM of 378 and 385
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 378 and 385 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 20790 as output. Here you can check the answer for Find the LCM of 378 and 385.
What is LCM of 378 and 385
Given Numbers are 378, 385
We can find the LCM of 378, 385 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 378 and 385
Multiples of 378 =378,756,1134,1512,1890,2268,2646,3024,3402,3780,4158,4536,4914,5292,5670,6048,6426,
Multiples of 385 =385,770,1155,1540,1925,2310,2695,3080,3465,3850,4235,4620,5005,5390,5775,6160,6545,
Now, get the least common multiple of 378, 385 which is 20790
So, the LCM of 378, 385 is 20790.
Least Common Multiple (LCM) of 378 and 385 with the help of Prime Factorisation
One method for determining the LCM of 378 and 385 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 385's prime factorization:
| 5 | 385 |
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 385 are 5, 7,11.
385 = 51×71×111
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, 5,11
.21×33×51×71×111 = 20790
This shows that the LCM of 378 and 385 is 20790.
How to Calculate the LCM of 378 and 385 Using Common Multiples
The first step in determining the Least Common Multiple of 378 and 385 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 378 and 385:
Lets look at the first ten multiples of these numbers, 378 and 385:
378,756,1134,1512,1890,2268,2646,3024,3402,6426 are the first ten multiples of 378.
385,770,1155,1540,1925,2310,2695,3080,3465,6545 are the first ten multiples of 385.
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 385, for example, are 4536, 6426, and 6160. 20790 is the least common multiple since it is the smallest.
378 and 385 have an LCM of 20790.
Least Common Multiple of 378 and 385 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 385, than apply into the LCM equation.
GCF(378,385) = 7
LCM(378,385) = ( 378 × 385) / 7
LCM(378,385) = 145530 / 7
LCM(378,385) = 20790
Related Least Common Multiples of 378
Related Least Common Multiples of 385
Frequently Asked Questions on LCM of 378 and 385
1. What is the LCM of 378 and 385?
The LCM of 378 and 385 is 20790.
2. How to find the lowest common multiple of 378 and 385?
To find the lowest common multiple of 378 and 385, we have to get the multip;es of both numbers and identify the least common multiple in them which is 20790.
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 385?
Answer: Factors of 385 are 1, 5, 7, 11, 35, 55, 77, 385. There are 8 integers that are factors of 385. The greatest factor of 385 is 385.
5. How to Find the LCM of 378 and 385?Answer:
Least Common Multiple of 378 and 385 = 20790
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 385
385 = 5 x 7 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 20790 = 2 x 3 x 3 x 3 x 5 x 7 x 11
Step 4: Therefore, the least common multiple of 378 and 385 is 20790.