LCM of 315 and 322
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 315 and 322 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 14490 as output. Here you can check the answer for Find the LCM of 315 and 322.
What is LCM of 315 and 322
Given Numbers are 315, 322
We can find the LCM of 315, 322 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 315 and 322
Multiples of 315 =315,630,945,1260,1575,1890,2205,2520,2835,3150,3465,3780,4095,4410,4725,5040,5355,
Multiples of 322 =322,644,966,1288,1610,1932,2254,2576,2898,3220,3542,3864,4186,4508,4830,5152,5474,
Now, get the least common multiple of 315, 322 which is 14490
So, the LCM of 315, 322 is 14490.
Least Common Multiple (LCM) of 315 and 322 with the help of Prime Factorisation
One method for determining the LCM of 315 and 322 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 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
And this is 322's prime factorization:
| 2 | 322 |
| 7 | 161 |
| 23 | 23 |
| 1 |
Prime factors of 322 are 2, 7,23.
322 = 21×71×231
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, 5,7, 2,23
.21×32×51×71×231 = 14490
This shows that the LCM of 315 and 322 is 14490.
How to Calculate the LCM of 315 and 322 Using Common Multiples
The first step in determining the Least Common Multiple of 315 and 322 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 315 and 322:
Lets look at the first ten multiples of these numbers, 315 and 322:
315,630,945,1260,1575,1890,2205,2520,2835,5355 are the first ten multiples of 315.
322,644,966,1288,1610,1932,2254,2576,2898,5474 are the first ten multiples of 322.
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 315 and 322, for example, are 3780, 5355, and 5152. 14490 is the least common multiple since it is the smallest.
315 and 322 have an LCM of 14490.
Least Common Multiple of 315 and 322 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315 and 322, than apply into the LCM equation.
GCF(315,322) = 7
LCM(315,322) = ( 315 × 322) / 7
LCM(315,322) = 101430 / 7
LCM(315,322) = 14490
Related Least Common Multiples of 315
Related Least Common Multiples of 322
Frequently Asked Questions on LCM of 315 and 322
1. What is the LCM of 315 and 322?
The LCM of 315 and 322 is 14490.
2. How to find the lowest common multiple of 315 and 322?
To find the lowest common multiple of 315 and 322, we have to get the multip;es of both numbers and identify the least common multiple in them which is 14490.
3. 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.
4. What are the Factors of 322?
Answer: Factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322. There are 8 integers that are factors of 322. The greatest factor of 322 is 322.
5. How to Find the LCM of 315 and 322?Answer:
Least Common Multiple of 315 and 322 = 14490
Step 1: Find the prime factorization of 315
315 = 3 x 3 x 5 x 7
Step 2: Find the prime factorization of 322
322 = 2 x 7 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14490 = 2 x 3 x 3 x 5 x 7 x 23
Step 4: Therefore, the least common multiple of 315 and 322 is 14490.