LCM of 312 and 318
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 312 and 318 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 16536 as output. Here you can check the answer for Find the LCM of 312 and 318.
What is LCM of 312 and 318
Given Numbers are 312, 318
We can find the LCM of 312, 318 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 312 and 318
Multiples of 312 =312,624,936,1248,1560,1872,2184,2496,2808,3120,3432,3744,4056,4368,4680,4992,5304,
Multiples of 318 =318,636,954,1272,1590,1908,2226,2544,2862,3180,3498,3816,4134,4452,4770,5088,5406,
Now, get the least common multiple of 312, 318 which is 16536
So, the LCM of 312, 318 is 16536.
Least Common Multiple (LCM) of 312 and 318 with the help of Prime Factorisation
One method for determining the LCM of 312 and 318 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 312's prime factorization:
| 2 | 312 |
| 2 | 156 |
| 2 | 78 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 312 are 2, 3,13.
312 = 23×31×131
And this is 318's prime factorization:
| 2 | 318 |
| 3 | 159 |
| 53 | 53 |
| 1 |
Prime factors of 318 are 2, 3,53.
318 = 21×31×531
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: 2, 3,13,53
.23×31×131×531 = 16536
This shows that the LCM of 312 and 318 is 16536.
How to Calculate the LCM of 312 and 318 Using Common Multiples
The first step in determining the Least Common Multiple of 312 and 318 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 312 and 318:
Lets look at the first ten multiples of these numbers, 312 and 318:
312,624,936,1248,1560,1872,2184,2496,2808,5304 are the first ten multiples of 312.
318,636,954,1272,1590,1908,2226,2544,2862,5406 are the first ten multiples of 318.
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 312 and 318, for example, are 3744, 5304, and 5088. 16536 is the least common multiple since it is the smallest.
312 and 318 have an LCM of 16536.
Least Common Multiple of 312 and 318 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 318, than apply into the LCM equation.
GCF(312,318) = 6
LCM(312,318) = ( 312 × 318) / 6
LCM(312,318) = 99216 / 6
LCM(312,318) = 16536
Related Least Common Multiples of 312
Related Least Common Multiples of 318
Frequently Asked Questions on LCM of 312 and 318
1. What is the LCM of 312 and 318?
The LCM of 312 and 318 is 16536.
2. How to find the lowest common multiple of 312 and 318?
To find the lowest common multiple of 312 and 318, we have to get the multip;es of both numbers and identify the least common multiple in them which is 16536.
3. What are the Factors of 312?
Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.
4. What are the Factors of 318?
Answer: Factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318. There are 8 integers that are factors of 318. The greatest factor of 318 is 318.
5. How to Find the LCM of 312 and 318?Answer:
Least Common Multiple of 312 and 318 = 16536
Step 1: Find the prime factorization of 312
312 = 2 x 2 x 2 x 3 x 13
Step 2: Find the prime factorization of 318
318 = 2 x 3 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 16536 = 2 x 2 x 2 x 3 x 13 x 53
Step 4: Therefore, the least common multiple of 312 and 318 is 16536.