LCM of 345 and 352
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 345 and 352 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 121440 as output. Here you can check the answer for Find the LCM of 345 and 352.
What is LCM of 345 and 352
Given Numbers are 345, 352
We can find the LCM of 345, 352 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 345 and 352
Multiples of 345 =345,690,1035,1380,1725,2070,2415,2760,3105,3450,3795,4140,4485,4830,5175,5520,5865,
Multiples of 352 =352,704,1056,1408,1760,2112,2464,2816,3168,3520,3872,4224,4576,4928,5280,5632,5984,
Now, get the least common multiple of 345, 352 which is 121440
So, the LCM of 345, 352 is 121440.
Least Common Multiple (LCM) of 345 and 352 with the help of Prime Factorisation
One method for determining the LCM of 345 and 352 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 352's prime factorization:
| 2 | 352 |
| 2 | 176 |
| 2 | 88 |
| 2 | 44 |
| 2 | 22 |
| 11 | 11 |
| 1 |
Prime factors of 352 are 2,11.
352 = 25×111
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: 3, 5,23, 2,11
.25×31×51×111×231 = 121440
This shows that the LCM of 345 and 352 is 121440.
How to Calculate the LCM of 345 and 352 Using Common Multiples
The first step in determining the Least Common Multiple of 345 and 352 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 345 and 352:
Lets look at the first ten multiples of these numbers, 345 and 352:
345,690,1035,1380,1725,2070,2415,2760,3105,5865 are the first ten multiples of 345.
352,704,1056,1408,1760,2112,2464,2816,3168,5984 are the first ten multiples of 352.
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 352, for example, are 4140, 5865, and 5632. 121440 is the least common multiple since it is the smallest.
345 and 352 have an LCM of 121440.
Least Common Multiple of 345 and 352 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 352, than apply into the LCM equation.
GCF(345,352) = 1
LCM(345,352) = ( 345 × 352) / 1
LCM(345,352) = 121440 / 1
LCM(345,352) = 121440
Related Least Common Multiples of 345
Related Least Common Multiples of 352
Frequently Asked Questions on LCM of 345 and 352
1. What is the LCM of 345 and 352?
The LCM of 345 and 352 is 121440.
2. How to find the lowest common multiple of 345 and 352?
To find the lowest common multiple of 345 and 352, we have to get the multip;es of both numbers and identify the least common multiple in them which is 121440.
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 352?
Answer: Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352. There are 12 integers that are factors of 352. The greatest factor of 352 is 352.
5. How to Find the LCM of 345 and 352?Answer:
Least Common Multiple of 345 and 352 = 121440
Step 1: Find the prime factorization of 345
345 = 3 x 5 x 23
Step 2: Find the prime factorization of 352
352 = 2 x 2 x 2 x 2 x 2 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 = 121440 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11 x 23
Step 4: Therefore, the least common multiple of 345 and 352 is 121440.