LCM of 306 and 312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 306 and 312 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 15912 as output. Here you can check the answer for Find the LCM of 306 and 312.
What is LCM of 306 and 312
Given Numbers are 306, 312
We can find the LCM of 306, 312 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 306 and 312
Multiples of 306 =306,612,918,1224,1530,1836,2142,2448,2754,3060,3366,3672,3978,4284,4590,4896,5202,
Multiples of 312 =312,624,936,1248,1560,1872,2184,2496,2808,3120,3432,3744,4056,4368,4680,4992,5304,
Now, get the least common multiple of 306, 312 which is 15912
So, the LCM of 306, 312 is 15912.
Least Common Multiple (LCM) of 306 and 312 with the help of Prime Factorisation
One method for determining the LCM of 306 and 312 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 306's prime factorization:
| 2 | 306 |
| 3 | 153 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 306 are 2, 3,17.
306 = 21×32×171
And this 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
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, 3,17,13
.23×32×131×171 = 15912
This shows that the LCM of 306 and 312 is 15912.
How to Calculate the LCM of 306 and 312 Using Common Multiples
The first step in determining the Least Common Multiple of 306 and 312 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 306 and 312:
Lets look at the first ten multiples of these numbers, 306 and 312:
306,612,918,1224,1530,1836,2142,2448,2754,5202 are the first ten multiples of 306.
312,624,936,1248,1560,1872,2184,2496,2808,5304 are the first ten multiples of 312.
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 306 and 312, for example, are 3672, 5202, and 4992. 15912 is the least common multiple since it is the smallest.
306 and 312 have an LCM of 15912.
Least Common Multiple of 306 and 312 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 306 and 312, than apply into the LCM equation.
GCF(306,312) = 6
LCM(306,312) = ( 306 × 312) / 6
LCM(306,312) = 95472 / 6
LCM(306,312) = 15912
Related Least Common Multiples of 306
Related Least Common Multiples of 312
Frequently Asked Questions on LCM of 306 and 312
1. What is the LCM of 306 and 312?
The LCM of 306 and 312 is 15912.
2. How to find the lowest common multiple of 306 and 312?
To find the lowest common multiple of 306 and 312, we have to get the multip;es of both numbers and identify the least common multiple in them which is 15912.
3. What are the Factors of 306?
Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.
4. 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.
5. How to Find the LCM of 306 and 312?Answer:
Least Common Multiple of 306 and 312 = 15912
Step 1: Find the prime factorization of 306
306 = 2 x 3 x 3 x 17
Step 2: Find the prime factorization of 312
312 = 2 x 2 x 2 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 15912 = 2 x 2 x 2 x 3 x 3 x 13 x 17
Step 4: Therefore, the least common multiple of 306 and 312 is 15912.