Given Numbers are 312, 317

We can find the LCM of 312, 317 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 312 and 317

Multiples of 312 =312,624,936,1248,1560,1872,2184,2496,2808,3120,3432,3744,4056,4368,4680,4992,5304,

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 312, 317 which is 98904

So, the LCM of 312, 317 is 98904.

One method for determining the LCM of 312 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 312's prime factorization:

Prime factors of 312 are 2, 3,13.

312 = 2³×3¹×13¹

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: 2, 3,13,317

2³×3¹×13¹×317¹ = 98904

This shows that the LCM of 312 and 317 is 98904.

The first step in determining the Least Common Multiple of 312 and 317 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 312 and 317:

Lets look at the first ten multiples of these numbers, 312 and 317:

312,624,936,1248,1560,1872,2184,2496,2808,5304 are the first ten multiples of 312.

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 312 and 317, for example, are 3744, 5304, and 5072. 98904 is the least common multiple since it is the smallest.

312 and 317 have an LCM of 98904.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 317, than apply into the LCM equation.

GCF(312,317) = 1
LCM(312,317) = ( 312 × 317) / 1
LCM(312,317) = 98904 / 1
LCM(312,317) = 98904

1. What is the LCM of 312 and 317?

The LCM of 312 and 317 is 98904.

2. How to find the lowest common multiple of 312 and 317?

To find the lowest common multiple of 312 and 317, we have to get the multip;es of both numbers and identify the least common multiple in them which is 98904.

3. What are the Factors of 312?

Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.

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 312 and 317 = 98904

Step 1: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

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 = 98904 = 2 x 2 x 2 x 3 x 13 x 317

Step 4: Therefore, the least common multiple of 312 and 317 is 98904.