LCM of 309 and 315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 309 and 315 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 32445 as output. Here you can check the answer for Find the LCM of 309 and 315.
What is LCM of 309 and 315
Given Numbers are 309, 315
We can find the LCM of 309, 315 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 309 and 315
Multiples of 309 =309,618,927,1236,1545,1854,2163,2472,2781,3090,3399,3708,4017,4326,4635,4944,5253,
Multiples of 315 =315,630,945,1260,1575,1890,2205,2520,2835,3150,3465,3780,4095,4410,4725,5040,5355,
Now, get the least common multiple of 309, 315 which is 32445
So, the LCM of 309, 315 is 32445.
Least Common Multiple (LCM) of 309 and 315 with the help of Prime Factorisation
One method for determining the LCM of 309 and 315 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 309's prime factorization:
| 3 | 309 |
| 103 | 103 |
| 1 |
Prime factors of 309 are 3,103.
309 = 31×1031
And this is 315's prime factorization:
| 3 | 315 |
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 315 are 3, 5,7.
315 = 32×51×71
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: 3,103, 5,7
.32×51×71×1031 = 32445
This shows that the LCM of 309 and 315 is 32445.
How to Calculate the LCM of 309 and 315 Using Common Multiples
The first step in determining the Least Common Multiple of 309 and 315 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 309 and 315:
Lets look at the first ten multiples of these numbers, 309 and 315:
309,618,927,1236,1545,1854,2163,2472,2781,5253 are the first ten multiples of 309.
315,630,945,1260,1575,1890,2205,2520,2835,5355 are the first ten multiples of 315.
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 309 and 315, for example, are 3708, 5253, and 5040. 32445 is the least common multiple since it is the smallest.
309 and 315 have an LCM of 32445.
Least Common Multiple of 309 and 315 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 309 and 315, than apply into the LCM equation.
GCF(309,315) = 3
LCM(309,315) = ( 309 × 315) / 3
LCM(309,315) = 97335 / 3
LCM(309,315) = 32445
Related Least Common Multiples of 309
Related Least Common Multiples of 315
Frequently Asked Questions on LCM of 309 and 315
1. What is the LCM of 309 and 315?
The LCM of 309 and 315 is 32445.
2. How to find the lowest common multiple of 309 and 315?
To find the lowest common multiple of 309 and 315, we have to get the multip;es of both numbers and identify the least common multiple in them which is 32445.
3. What are the Factors of 309?
Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.
4. What are the Factors of 315?
Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.
5. How to Find the LCM of 309 and 315?Answer:
Least Common Multiple of 309 and 315 = 32445
Step 1: Find the prime factorization of 309
309 = 3 x 103
Step 2: Find the prime factorization of 315
315 = 3 x 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 32445 = 3 x 3 x 5 x 7 x 103
Step 4: Therefore, the least common multiple of 309 and 315 is 32445.