Given Numbers are 307, 314

We can find the LCM of 307, 314 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 307 and 314

Multiples of 307 =307,614,921,1228,1535,1842,2149,2456,2763,3070,3377,3684,3991,4298,4605,4912,5219,

Multiples of 314 =314,628,942,1256,1570,1884,2198,2512,2826,3140,3454,3768,4082,4396,4710,5024,5338,

Now, get the least common multiple of 307, 314 which is 96398

So, the LCM of 307, 314 is 96398.

One method for determining the LCM of 307 and 314 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 307's prime factorization:

Prime factors of 307 are 307.

307 = 307¹

And this is 314's prime factorization:

Prime factors of 314 are 2,157.

314 = 2¹×157¹

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:307, 2,157

2¹×157¹×307¹ = 96398

This shows that the LCM of 307 and 314 is 96398.

The first step in determining the Least Common Multiple of 307 and 314 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 307 and 314:

Lets look at the first ten multiples of these numbers, 307 and 314:

307,614,921,1228,1535,1842,2149,2456,2763,5219 are the first ten multiples of 307.

314,628,942,1256,1570,1884,2198,2512,2826,5338 are the first ten multiples of 314.

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 307 and 314, for example, are 3684, 5219, and 5024. 96398 is the least common multiple since it is the smallest.

307 and 314 have an LCM of 96398.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 307 and 314, than apply into the LCM equation.

GCF(307,314) = 1
LCM(307,314) = ( 307 × 314) / 1
LCM(307,314) = 96398 / 1
LCM(307,314) = 96398

1. What is the LCM of 307 and 314?

The LCM of 307 and 314 is 96398.

2. How to find the lowest common multiple of 307 and 314?

To find the lowest common multiple of 307 and 314, we have to get the multip;es of both numbers and identify the least common multiple in them which is 96398.

3. What are the Factors of 307?

Answer: Factors of 307 are 1, 307. There are 2 integers that are factors of 307. The greatest factor of 307 is 307.

4. What are the Factors of 314?

Answer: Factors of 314 are 1, 2, 157, 314. There are 4 integers that are factors of 314. The greatest factor of 314 is 314.

Answer:

Least Common Multiple of 307 and 314 = 96398

Step 1: Find the prime factorization of 307

307 = 307

Step 2: Find the prime factorization of 314

314 = 2 x 157

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 96398 = 2 x 157 x 307

Step 4: Therefore, the least common multiple of 307 and 314 is 96398.