LCM of 345 and 351
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 345 and 351 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 40365 as output. Here you can check the answer for Find the LCM of 345 and 351.
What is LCM of 345 and 351
Given Numbers are 345, 351
We can find the LCM of 345, 351 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 345 and 351
Multiples of 345 =345,690,1035,1380,1725,2070,2415,2760,3105,3450,3795,4140,4485,4830,5175,5520,5865,
Multiples of 351 =351,702,1053,1404,1755,2106,2457,2808,3159,3510,3861,4212,4563,4914,5265,5616,5967,
Now, get the least common multiple of 345, 351 which is 40365
So, the LCM of 345, 351 is 40365.
Least Common Multiple (LCM) of 345 and 351 with the help of Prime Factorisation
One method for determining the LCM of 345 and 351 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 345's prime factorization:
| 3 | 345 |
| 5 | 115 |
| 23 | 23 |
| 1 |
Prime factors of 345 are 3, 5,23.
345 = 31×51×231
And this is 351's prime factorization:
| 3 | 351 |
| 3 | 117 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 351 are 3,13.
351 = 33×131
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: 3, 5,23,13
.33×51×131×231 = 40365
This shows that the LCM of 345 and 351 is 40365.
How to Calculate the LCM of 345 and 351 Using Common Multiples
The first step in determining the Least Common Multiple of 345 and 351 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 345 and 351:
Lets look at the first ten multiples of these numbers, 345 and 351:
345,690,1035,1380,1725,2070,2415,2760,3105,5865 are the first ten multiples of 345.
351,702,1053,1404,1755,2106,2457,2808,3159,5967 are the first ten multiples of 351.
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 345 and 351, for example, are 4140, 5865, and 5616. 40365 is the least common multiple since it is the smallest.
345 and 351 have an LCM of 40365.
Least Common Multiple of 345 and 351 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 351, than apply into the LCM equation.
GCF(345,351) = 3
LCM(345,351) = ( 345 × 351) / 3
LCM(345,351) = 121095 / 3
LCM(345,351) = 40365
Related Least Common Multiples of 345
Related Least Common Multiples of 351
Frequently Asked Questions on LCM of 345 and 351
1. What is the LCM of 345 and 351?
The LCM of 345 and 351 is 40365.
2. How to find the lowest common multiple of 345 and 351?
To find the lowest common multiple of 345 and 351, we have to get the multip;es of both numbers and identify the least common multiple in them which is 40365.
3. What are the Factors of 345?
Answer: Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345. There are 8 integers that are factors of 345. The greatest factor of 345 is 345.
4. What are the Factors of 351?
Answer: Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351. There are 8 integers that are factors of 351. The greatest factor of 351 is 351.
5. How to Find the LCM of 345 and 351?Answer:
Least Common Multiple of 345 and 351 = 40365
Step 1: Find the prime factorization of 345
345 = 3 x 5 x 23
Step 2: Find the prime factorization of 351
351 = 3 x 3 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 40365 = 3 x 3 x 3 x 5 x 13 x 23
Step 4: Therefore, the least common multiple of 345 and 351 is 40365.