Given Numbers are 306, 314

We can find the LCM of 306, 314 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 306 and 314

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

Multiples of 314 =314,628,942,1256,1570,1884,2198,2512,2826,3140,3454,3768,4082,4396,4710,5024,5338,

Now, get the least common multiple of 306, 314 which is 48042

So, the LCM of 306, 314 is 48042.

One method for determining the LCM of 306 and 314 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 314's prime factorization:

Prime factors of 314 are 2,157.

314 = 2¹×157¹

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, 3,17,157

2¹×3²×17¹×157¹ = 48042

This shows that the LCM of 306 and 314 is 48042.

The first step in determining the Least Common Multiple of 306 and 314 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 306 and 314:

Lets look at the first ten multiples of these numbers, 306 and 314:

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

314,628,942,1256,1570,1884,2198,2512,2826,5338 are the first ten multiples of 314.

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 314, for example, are 3672, 5202, and 5024. 48042 is the least common multiple since it is the smallest.

306 and 314 have an LCM of 48042.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 306 and 314, than apply into the LCM equation.

GCF(306,314) = 2
LCM(306,314) = ( 306 × 314) / 2
LCM(306,314) = 96084 / 2
LCM(306,314) = 48042

1. What is the LCM of 306 and 314?

The LCM of 306 and 314 is 48042.

2. How to find the lowest common multiple of 306 and 314?

To find the lowest common multiple of 306 and 314, we have to get the multip;es of both numbers and identify the least common multiple in them which is 48042.

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 314?

Answer: Factors of 314 are 1, 2, 157, 314. There are 4 integers that are factors of 314. The greatest factor of 314 is 314.

Answer:

Least Common Multiple of 306 and 314 = 48042

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 314

314 = 2 x 157

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

LCM = 48042 = 2 x 3 x 3 x 17 x 157

Step 4: Therefore, the least common multiple of 306 and 314 is 48042.