Given Numbers are 314, 320

We can find the LCM of 314, 320 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 314 and 320

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

Multiples of 320 =320,640,960,1280,1600,1920,2240,2560,2880,3200,3520,3840,4160,4480,4800,5120,5440,

Now, get the least common multiple of 314, 320 which is 50240

So, the LCM of 314, 320 is 50240.

One method for determining the LCM of 314 and 320 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 320's prime factorization:

Prime factors of 320 are 2,5.

320 = 2⁶×5¹

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: 2,157,5

2⁶×5¹×157¹ = 50240

This shows that the LCM of 314 and 320 is 50240.

The first step in determining the Least Common Multiple of 314 and 320 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 314 and 320:

Lets look at the first ten multiples of these numbers, 314 and 320:

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

320,640,960,1280,1600,1920,2240,2560,2880,5440 are the first ten multiples of 320.

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 320, for example, are 3768, 5338, and 5120. 50240 is the least common multiple since it is the smallest.

314 and 320 have an LCM of 50240.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 320, than apply into the LCM equation.

GCF(314,320) = 2
LCM(314,320) = ( 314 × 320) / 2
LCM(314,320) = 100480 / 2
LCM(314,320) = 50240

1. What is the LCM of 314 and 320?

The LCM of 314 and 320 is 50240.

2. How to find the lowest common multiple of 314 and 320?

To find the lowest common multiple of 314 and 320, we have to get the multip;es of both numbers and identify the least common multiple in them which is 50240.

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 320?

Answer: Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. There are 14 integers that are factors of 320. The greatest factor of 320 is 320.

Answer:

Least Common Multiple of 314 and 320 = 50240

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 320

320 = 2 x 2 x 2 x 2 x 2 x 2 x 5

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

LCM = 50240 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 157

Step 4: Therefore, the least common multiple of 314 and 320 is 50240.