Given Numbers are 338, 345

We can find the LCM of 338, 345 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 338 and 345

Multiples of 338 =338,676,1014,1352,1690,2028,2366,2704,3042,3380,3718,4056,4394,4732,5070,5408,5746,

Multiples of 345 =345,690,1035,1380,1725,2070,2415,2760,3105,3450,3795,4140,4485,4830,5175,5520,5865,

Now, get the least common multiple of 338, 345 which is 116610

So, the LCM of 338, 345 is 116610.

One method for determining the LCM of 338 and 345 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 338's prime factorization:

Prime factors of 338 are 2,13.

338 = 2¹×13²

And this is 345's prime factorization:

Prime factors of 345 are 3, 5,23.

345 = 3¹×5¹×23¹

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: 2,13, 3, 5,23

2¹×3¹×5¹×13²×23¹ = 116610

This shows that the LCM of 338 and 345 is 116610.

The first step in determining the Least Common Multiple of 338 and 345 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 338 and 345:

Lets look at the first ten multiples of these numbers, 338 and 345:

338,676,1014,1352,1690,2028,2366,2704,3042,5746 are the first ten multiples of 338.

345,690,1035,1380,1725,2070,2415,2760,3105,5865 are the first ten multiples of 345.

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 338 and 345, for example, are 4056, 5746, and 5520. 116610 is the least common multiple since it is the smallest.

338 and 345 have an LCM of 116610.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 338 and 345, than apply into the LCM equation.

GCF(338,345) = 1
LCM(338,345) = ( 338 × 345) / 1
LCM(338,345) = 116610 / 1
LCM(338,345) = 116610

1. What is the LCM of 338 and 345?

The LCM of 338 and 345 is 116610.

2. How to find the lowest common multiple of 338 and 345?

To find the lowest common multiple of 338 and 345, we have to get the multip;es of both numbers and identify the least common multiple in them which is 116610.

3. What are the Factors of 338?

Answer: Factors of 338 are 1, 2, 13, 26, 169, 338. There are 6 integers that are factors of 338. The greatest factor of 338 is 338.

4. What are the Factors of 345?

Answer: Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345. There are 8 integers that are factors of 345. The greatest factor of 345 is 345.

Answer:

Least Common Multiple of 338 and 345 = 116610

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

Step 2: Find the prime factorization of 345

345 = 3 x 5 x 23

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

LCM = 116610 = 2 x 3 x 5 x 13 x 13 x 23

Step 4: Therefore, the least common multiple of 338 and 345 is 116610.