Given Numbers are 306, 311

We can find the LCM of 306, 311 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 306 and 311

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

Multiples of 311 =311,622,933,1244,1555,1866,2177,2488,2799,3110,3421,3732,4043,4354,4665,4976,5287,

Now, get the least common multiple of 306, 311 which is 95166

So, the LCM of 306, 311 is 95166.

One method for determining the LCM of 306 and 311 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 306's prime factorization:

Prime factors of 306 are 2, 3,17.

306 = 2¹×3²×17¹

And this is 311's prime factorization:

Prime factors of 311 are 311.

311 = 311¹

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, 3,17,311

2¹×3²×17¹×311¹ = 95166

This shows that the LCM of 306 and 311 is 95166.

The first step in determining the Least Common Multiple of 306 and 311 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 306 and 311:

Lets look at the first ten multiples of these numbers, 306 and 311:

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

311,622,933,1244,1555,1866,2177,2488,2799,5287 are the first ten multiples of 311.

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 306 and 311, for example, are 3672, 5202, and 4976. 95166 is the least common multiple since it is the smallest.

306 and 311 have an LCM of 95166.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 306 and 311, than apply into the LCM equation.

GCF(306,311) = 1
LCM(306,311) = ( 306 × 311) / 1
LCM(306,311) = 95166 / 1
LCM(306,311) = 95166

1. What is the LCM of 306 and 311?

The LCM of 306 and 311 is 95166.

2. How to find the lowest common multiple of 306 and 311?

To find the lowest common multiple of 306 and 311, we have to get the multip;es of both numbers and identify the least common multiple in them which is 95166.

3. 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.

4. What are the Factors of 311?

Answer: Factors of 311 are 1, 311. There are 2 integers that are factors of 311. The greatest factor of 311 is 311.

Answer:

Least Common Multiple of 306 and 311 = 95166

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 311

311 = 311

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

LCM = 95166 = 2 x 3 x 3 x 17 x 311

Step 4: Therefore, the least common multiple of 306 and 311 is 95166.