Given Numbers are 314, 321

We can find the LCM of 314, 321 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 314 and 321

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

Multiples of 321 =321,642,963,1284,1605,1926,2247,2568,2889,3210,3531,3852,4173,4494,4815,5136,5457,

Now, get the least common multiple of 314, 321 which is 100794

So, the LCM of 314, 321 is 100794.

One method for determining the LCM of 314 and 321 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 314's prime factorization:

Prime factors of 314 are 2,157.

314 = 2¹×157¹

And this is 321's prime factorization:

Prime factors of 321 are 3,107.

321 = 3¹×107¹

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: 2,157, 3,107

2¹×3¹×107¹×157¹ = 100794

This shows that the LCM of 314 and 321 is 100794.

The first step in determining the Least Common Multiple of 314 and 321 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 314 and 321:

Lets look at the first ten multiples of these numbers, 314 and 321:

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

321,642,963,1284,1605,1926,2247,2568,2889,5457 are the first ten multiples of 321.

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 314 and 321, for example, are 3768, 5338, and 5136. 100794 is the least common multiple since it is the smallest.

314 and 321 have an LCM of 100794.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 321, than apply into the LCM equation.

GCF(314,321) = 1
LCM(314,321) = ( 314 × 321) / 1
LCM(314,321) = 100794 / 1
LCM(314,321) = 100794

1. What is the LCM of 314 and 321?

The LCM of 314 and 321 is 100794.

2. How to find the lowest common multiple of 314 and 321?

To find the lowest common multiple of 314 and 321, we have to get the multip;es of both numbers and identify the least common multiple in them which is 100794.

3. 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.

4. What are the Factors of 321?

Answer: Factors of 321 are 1, 3, 107, 321. There are 4 integers that are factors of 321. The greatest factor of 321 is 321.

Answer:

Least Common Multiple of 314 and 321 = 100794

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 321

321 = 3 x 107

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

LCM = 100794 = 2 x 3 x 107 x 157

Step 4: Therefore, the least common multiple of 314 and 321 is 100794.