LCM of 308 and 312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 308 and 312 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 24024 as output. Here you can check the answer for Find the LCM of 308 and 312.
What is LCM of 308 and 312
Given Numbers are 308, 312
We can find the LCM of 308, 312 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 308 and 312
Multiples of 308 =308,616,924,1232,1540,1848,2156,2464,2772,3080,3388,3696,4004,4312,4620,4928,5236,
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 308, 312 which is 24024
So, the LCM of 308, 312 is 24024.
Least Common Multiple (LCM) of 308 and 312 with the help of Prime Factorisation
One method for determining the LCM of 308 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 308's prime factorization:
| 2 | 308 |
| 2 | 154 |
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 308 are 2, 7,11.
308 = 22×71×111
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, 7,11, 3,13
.23×31×71×111×131 = 24024
This shows that the LCM of 308 and 312 is 24024.
How to Calculate the LCM of 308 and 312 Using Common Multiples
The first step in determining the Least Common Multiple of 308 and 312 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 308 and 312:
Lets look at the first ten multiples of these numbers, 308 and 312:
308,616,924,1232,1540,1848,2156,2464,2772,5236 are the first ten multiples of 308.
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 308 and 312, for example, are 3696, 5236, and 4992. 24024 is the least common multiple since it is the smallest.
308 and 312 have an LCM of 24024.
Least Common Multiple of 308 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 308 and 312, than apply into the LCM equation.
GCF(308,312) = 4
LCM(308,312) = ( 308 × 312) / 4
LCM(308,312) = 96096 / 4
LCM(308,312) = 24024
Related Least Common Multiples of 308
Related Least Common Multiples of 312
Frequently Asked Questions on LCM of 308 and 312
1. What is the LCM of 308 and 312?
The LCM of 308 and 312 is 24024.
2. How to find the lowest common multiple of 308 and 312?
To find the lowest common multiple of 308 and 312, we have to get the multip;es of both numbers and identify the least common multiple in them which is 24024.
3. What are the Factors of 308?
Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.
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 308 and 312?Answer:
Least Common Multiple of 308 and 312 = 24024
Step 1: Find the prime factorization of 308
308 = 2 x 2 x 7 x 11
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 = 24024 = 2 x 2 x 2 x 3 x 7 x 11 x 13
Step 4: Therefore, the least common multiple of 308 and 312 is 24024.