Given Numbers are 305, 313

We can find the LCM of 305, 313 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 305 and 313

Multiples of 305 =305,610,915,1220,1525,1830,2135,2440,2745,3050,3355,3660,3965,4270,4575,4880,5185,

Multiples of 313 =313,626,939,1252,1565,1878,2191,2504,2817,3130,3443,3756,4069,4382,4695,5008,5321,

Now, get the least common multiple of 305, 313 which is 95465

So, the LCM of 305, 313 is 95465.

One method for determining the LCM of 305 and 313 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 305's prime factorization:

Prime factors of 305 are 5,61.

305 = 5¹×61¹

And this is 313's prime factorization:

Prime factors of 313 are 313.

313 = 313¹

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: 5,61,313

5¹×61¹×313¹ = 95465

This shows that the LCM of 305 and 313 is 95465.

The first step in determining the Least Common Multiple of 305 and 313 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 305 and 313:

Lets look at the first ten multiples of these numbers, 305 and 313:

305,610,915,1220,1525,1830,2135,2440,2745,5185 are the first ten multiples of 305.

313,626,939,1252,1565,1878,2191,2504,2817,5321 are the first ten multiples of 313.

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 305 and 313, for example, are 3660, 5185, and 5008. 95465 is the least common multiple since it is the smallest.

305 and 313 have an LCM of 95465.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 313, than apply into the LCM equation.

GCF(305,313) = 1
LCM(305,313) = ( 305 × 313) / 1
LCM(305,313) = 95465 / 1
LCM(305,313) = 95465

1. What is the LCM of 305 and 313?

The LCM of 305 and 313 is 95465.

2. How to find the lowest common multiple of 305 and 313?

To find the lowest common multiple of 305 and 313, we have to get the multip;es of both numbers and identify the least common multiple in them which is 95465.

3. What are the Factors of 305?

Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.

4. What are the Factors of 313?

Answer: Factors of 313 are 1, 313. There are 2 integers that are factors of 313. The greatest factor of 313 is 313.

Answer:

Least Common Multiple of 305 and 313 = 95465

Step 1: Find the prime factorization of 305

305 = 5 x 61

Step 2: Find the prime factorization of 313

313 = 313

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

LCM = 95465 = 5 x 61 x 313

Step 4: Therefore, the least common multiple of 305 and 313 is 95465.