Given Numbers are 309, 317

We can find the LCM of 309, 317 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 309 and 317

Multiples of 309 =309,618,927,1236,1545,1854,2163,2472,2781,3090,3399,3708,4017,4326,4635,4944,5253,

Multiples of 317 =317,634,951,1268,1585,1902,2219,2536,2853,3170,3487,3804,4121,4438,4755,5072,5389,

Now, get the least common multiple of 309, 317 which is 97953

So, the LCM of 309, 317 is 97953.

One method for determining the LCM of 309 and 317 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 309's prime factorization:

Prime factors of 309 are 3,103.

309 = 3¹×103¹

And this is 317's prime factorization:

Prime factors of 317 are 317.

317 = 317¹

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: 3,103,317

3¹×103¹×317¹ = 97953

This shows that the LCM of 309 and 317 is 97953.

The first step in determining the Least Common Multiple of 309 and 317 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 309 and 317:

Lets look at the first ten multiples of these numbers, 309 and 317:

309,618,927,1236,1545,1854,2163,2472,2781,5253 are the first ten multiples of 309.

317,634,951,1268,1585,1902,2219,2536,2853,5389 are the first ten multiples of 317.

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 309 and 317, for example, are 3708, 5253, and 5072. 97953 is the least common multiple since it is the smallest.

309 and 317 have an LCM of 97953.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 309 and 317, than apply into the LCM equation.

GCF(309,317) = 1
LCM(309,317) = ( 309 × 317) / 1
LCM(309,317) = 97953 / 1
LCM(309,317) = 97953

1. What is the LCM of 309 and 317?

The LCM of 309 and 317 is 97953.

2. How to find the lowest common multiple of 309 and 317?

To find the lowest common multiple of 309 and 317, we have to get the multip;es of both numbers and identify the least common multiple in them which is 97953.

3. What are the Factors of 309?

Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.

4. What are the Factors of 317?

Answer: Factors of 317 are 1, 317. There are 2 integers that are factors of 317. The greatest factor of 317 is 317.

Answer:

Least Common Multiple of 309 and 317 = 97953

Step 1: Find the prime factorization of 309

309 = 3 x 103

Step 2: Find the prime factorization of 317

317 = 317

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

LCM = 97953 = 3 x 103 x 317

Step 4: Therefore, the least common multiple of 309 and 317 is 97953.