Given Numbers are 309, 314

We can find the LCM of 309, 314 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 309 and 314

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

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 309, 314 which is 97026

So, the LCM of 309, 314 is 97026.

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

Prime factors of 309 are 3,103.

309 = 3¹×103¹

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: 3,103, 2,157

2¹×3¹×103¹×157¹ = 97026

This shows that the LCM of 309 and 314 is 97026.

The first step in determining the Least Common Multiple of 309 and 314 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 309 and 314:

Lets look at the first ten multiples of these numbers, 309 and 314:

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

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 309 and 314, for example, are 3708, 5253, and 5024. 97026 is the least common multiple since it is the smallest.

309 and 314 have an LCM of 97026.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 309 and 314, than apply into the LCM equation.

GCF(309,314) = 1
LCM(309,314) = ( 309 × 314) / 1
LCM(309,314) = 97026 / 1
LCM(309,314) = 97026

1. What is the LCM of 309 and 314?

The LCM of 309 and 314 is 97026.

2. How to find the lowest common multiple of 309 and 314?

To find the lowest common multiple of 309 and 314, we have to get the multip;es of both numbers and identify the least common multiple in them which is 97026.

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 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 309 and 314 = 97026

Step 1: Find the prime factorization of 309

309 = 3 x 103

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 = 97026 = 2 x 3 x 103 x 157

Step 4: Therefore, the least common multiple of 309 and 314 is 97026.