Given Numbers are 338, 342

We can find the LCM of 338, 342 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 338 and 342

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

Multiples of 342 =342,684,1026,1368,1710,2052,2394,2736,3078,3420,3762,4104,4446,4788,5130,5472,5814,

Now, get the least common multiple of 338, 342 which is 57798

So, the LCM of 338, 342 is 57798.

One method for determining the LCM of 338 and 342 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 342's prime factorization:

Prime factors of 342 are 2, 3,19.

342 = 2¹×3²×19¹

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, 3,19

2¹×3²×13²×19¹ = 57798

This shows that the LCM of 338 and 342 is 57798.

The first step in determining the Least Common Multiple of 338 and 342 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 338 and 342:

Lets look at the first ten multiples of these numbers, 338 and 342:

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

342,684,1026,1368,1710,2052,2394,2736,3078,5814 are the first ten multiples of 342.

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 342, for example, are 4056, 5746, and 5472. 57798 is the least common multiple since it is the smallest.

338 and 342 have an LCM of 57798.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 338 and 342, than apply into the LCM equation.

GCF(338,342) = 2
LCM(338,342) = ( 338 × 342) / 2
LCM(338,342) = 115596 / 2
LCM(338,342) = 57798

1. What is the LCM of 338 and 342?

The LCM of 338 and 342 is 57798.

2. How to find the lowest common multiple of 338 and 342?

To find the lowest common multiple of 338 and 342, we have to get the multip;es of both numbers and identify the least common multiple in them which is 57798.

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 342?

Answer: Factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342. There are 12 integers that are factors of 342. The greatest factor of 342 is 342.

Answer:

Least Common Multiple of 338 and 342 = 57798

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

Step 2: Find the prime factorization of 342

342 = 2 x 3 x 3 x 19

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

LCM = 57798 = 2 x 3 x 3 x 13 x 13 x 19

Step 4: Therefore, the least common multiple of 338 and 342 is 57798.