LCM of 319 and 324
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 319 and 324 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 103356 as output. Here you can check the answer for Find the LCM of 319 and 324.
What is LCM of 319 and 324
Given Numbers are 319, 324
We can find the LCM of 319, 324 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 319 and 324
Multiples of 319 =319,638,957,1276,1595,1914,2233,2552,2871,3190,3509,3828,4147,4466,4785,5104,5423,
Multiples of 324 =324,648,972,1296,1620,1944,2268,2592,2916,3240,3564,3888,4212,4536,4860,5184,5508,
Now, get the least common multiple of 319, 324 which is 103356
So, the LCM of 319, 324 is 103356.
Least Common Multiple (LCM) of 319 and 324 with the help of Prime Factorisation
One method for determining the LCM of 319 and 324 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 319's prime factorization:
| 11 | 319 |
| 29 | 29 |
| 1 |
Prime factors of 319 are 11,29.
319 = 111×291
And this is 324's prime factorization:
| 2 | 324 |
| 2 | 162 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 324 are 2,3.
324 = 22×34
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: 11,29, 2,3
.22×34×111×291 = 103356
This shows that the LCM of 319 and 324 is 103356.
How to Calculate the LCM of 319 and 324 Using Common Multiples
The first step in determining the Least Common Multiple of 319 and 324 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 319 and 324:
Lets look at the first ten multiples of these numbers, 319 and 324:
319,638,957,1276,1595,1914,2233,2552,2871,5423 are the first ten multiples of 319.
324,648,972,1296,1620,1944,2268,2592,2916,5508 are the first ten multiples of 324.
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 319 and 324, for example, are 3828, 5423, and 5184. 103356 is the least common multiple since it is the smallest.
319 and 324 have an LCM of 103356.
Least Common Multiple of 319 and 324 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 319 and 324, than apply into the LCM equation.
GCF(319,324) = 1
LCM(319,324) = ( 319 × 324) / 1
LCM(319,324) = 103356 / 1
LCM(319,324) = 103356
Related Least Common Multiples of 319
Related Least Common Multiples of 324
Frequently Asked Questions on LCM of 319 and 324
1. What is the LCM of 319 and 324?
The LCM of 319 and 324 is 103356.
2. How to find the lowest common multiple of 319 and 324?
To find the lowest common multiple of 319 and 324, we have to get the multip;es of both numbers and identify the least common multiple in them which is 103356.
3. What are the Factors of 319?
Answer: Factors of 319 are 1, 11, 29, 319. There are 4 integers that are factors of 319. The greatest factor of 319 is 319.
4. What are the Factors of 324?
Answer: Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. There are 15 integers that are factors of 324. The greatest factor of 324 is 324.
5. How to Find the LCM of 319 and 324?Answer:
Least Common Multiple of 319 and 324 = 103356
Step 1: Find the prime factorization of 319
319 = 11 x 29
Step 2: Find the prime factorization of 324
324 = 2 x 2 x 3 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 103356 = 2 x 2 x 3 x 3 x 3 x 3 x 11 x 29
Step 4: Therefore, the least common multiple of 319 and 324 is 103356.