Given Numbers are 315, 321

We can find the LCM of 315, 321 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 315 and 321

Multiples of 315 =315,630,945,1260,1575,1890,2205,2520,2835,3150,3465,3780,4095,4410,4725,5040,5355,

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 315, 321 which is 33705

So, the LCM of 315, 321 is 33705.

One method for determining the LCM of 315 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 315's prime factorization:

Prime factors of 315 are 3, 5,7.

315 = 3²×5¹×7¹

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: 3, 5,7,107

3²×5¹×7¹×107¹ = 33705

This shows that the LCM of 315 and 321 is 33705.

The first step in determining the Least Common Multiple of 315 and 321 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 315 and 321:

Lets look at the first ten multiples of these numbers, 315 and 321:

315,630,945,1260,1575,1890,2205,2520,2835,5355 are the first ten multiples of 315.

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 315 and 321, for example, are 3780, 5355, and 5136. 33705 is the least common multiple since it is the smallest.

315 and 321 have an LCM of 33705.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315 and 321, than apply into the LCM equation.

GCF(315,321) = 3
LCM(315,321) = ( 315 × 321) / 3
LCM(315,321) = 101115 / 3
LCM(315,321) = 33705

1. What is the LCM of 315 and 321?

The LCM of 315 and 321 is 33705.

2. How to find the lowest common multiple of 315 and 321?

To find the lowest common multiple of 315 and 321, we have to get the multip;es of both numbers and identify the least common multiple in them which is 33705.

3. What are the Factors of 315?

Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.

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 315 and 321 = 33705

Step 1: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

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 = 33705 = 3 x 3 x 5 x 7 x 107

Step 4: Therefore, the least common multiple of 315 and 321 is 33705.