Given Numbers are 301, 305

We can find the LCM of 301, 305 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 301 and 305

Multiples of 301 =301,602,903,1204,1505,1806,2107,2408,2709,3010,3311,3612,3913,4214,4515,4816,5117,

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

Now, get the least common multiple of 301, 305 which is 91805

So, the LCM of 301, 305 is 91805.

One method for determining the LCM of 301 and 305 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 301's prime factorization:

Prime factors of 301 are 7,43.

301 = 7¹×43¹

And this is 305's prime factorization:

Prime factors of 305 are 5,61.

305 = 5¹×61¹

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: 7,43, 5,61

5¹×7¹×43¹×61¹ = 91805

This shows that the LCM of 301 and 305 is 91805.

The first step in determining the Least Common Multiple of 301 and 305 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 301 and 305:

Lets look at the first ten multiples of these numbers, 301 and 305:

301,602,903,1204,1505,1806,2107,2408,2709,5117 are the first ten multiples of 301.

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

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 301 and 305, for example, are 3612, 5117, and 4880. 91805 is the least common multiple since it is the smallest.

301 and 305 have an LCM of 91805.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 301 and 305, than apply into the LCM equation.

GCF(301,305) = 1
LCM(301,305) = ( 301 × 305) / 1
LCM(301,305) = 91805 / 1
LCM(301,305) = 91805

1. What is the LCM of 301 and 305?

The LCM of 301 and 305 is 91805.

2. How to find the lowest common multiple of 301 and 305?

To find the lowest common multiple of 301 and 305, we have to get the multip;es of both numbers and identify the least common multiple in them which is 91805.

3. What are the Factors of 301?

Answer: Factors of 301 are 1, 7, 43, 301. There are 4 integers that are factors of 301. The greatest factor of 301 is 301.

4. 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.

Answer:

Least Common Multiple of 301 and 305 = 91805

Step 1: Find the prime factorization of 301

301 = 7 x 43

Step 2: Find the prime factorization of 305

305 = 5 x 61

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

LCM = 91805 = 5 x 7 x 43 x 61

Step 4: Therefore, the least common multiple of 301 and 305 is 91805.