Given Numbers are 301, 306

We can find the LCM of 301, 306 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 301 and 306

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

Multiples of 306 =306,612,918,1224,1530,1836,2142,2448,2754,3060,3366,3672,3978,4284,4590,4896,5202,

Now, get the least common multiple of 301, 306 which is 92106

So, the LCM of 301, 306 is 92106.

One method for determining the LCM of 301 and 306 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 306's prime factorization:

Prime factors of 306 are 2, 3,17.

306 = 2¹×3²×17¹

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, 2, 3,17

2¹×3²×7¹×17¹×43¹ = 92106

This shows that the LCM of 301 and 306 is 92106.

The first step in determining the Least Common Multiple of 301 and 306 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 301 and 306:

Lets look at the first ten multiples of these numbers, 301 and 306:

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

306,612,918,1224,1530,1836,2142,2448,2754,5202 are the first ten multiples of 306.

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 306, for example, are 3612, 5117, and 4896. 92106 is the least common multiple since it is the smallest.

301 and 306 have an LCM of 92106.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 301 and 306, than apply into the LCM equation.

GCF(301,306) = 1
LCM(301,306) = ( 301 × 306) / 1
LCM(301,306) = 92106 / 1
LCM(301,306) = 92106

1. What is the LCM of 301 and 306?

The LCM of 301 and 306 is 92106.

2. How to find the lowest common multiple of 301 and 306?

To find the lowest common multiple of 301 and 306, we have to get the multip;es of both numbers and identify the least common multiple in them which is 92106.

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 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

Answer:

Least Common Multiple of 301 and 306 = 92106

Step 1: Find the prime factorization of 301

301 = 7 x 43

Step 2: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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

LCM = 92106 = 2 x 3 x 3 x 7 x 17 x 43

Step 4: Therefore, the least common multiple of 301 and 306 is 92106.