Given Numbers are 342, 348

We can find the LCM of 342, 348 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 342 and 348

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

Multiples of 348 =348,696,1044,1392,1740,2088,2436,2784,3132,3480,3828,4176,4524,4872,5220,5568,5916,

Now, get the least common multiple of 342, 348 which is 19836

So, the LCM of 342, 348 is 19836.

One method for determining the LCM of 342 and 348 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 342's prime factorization:

Prime factors of 342 are 2, 3,19.

342 = 2¹×3²×19¹

And this is 348's prime factorization:

Prime factors of 348 are 2, 3,29.

348 = 2²×3¹×29¹

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, 3,19,29

2²×3²×19¹×29¹ = 19836

This shows that the LCM of 342 and 348 is 19836.

The first step in determining the Least Common Multiple of 342 and 348 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 342 and 348:

Lets look at the first ten multiples of these numbers, 342 and 348:

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

348,696,1044,1392,1740,2088,2436,2784,3132,5916 are the first ten multiples of 348.

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 342 and 348, for example, are 4104, 5814, and 5568. 19836 is the least common multiple since it is the smallest.

342 and 348 have an LCM of 19836.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 342 and 348, than apply into the LCM equation.

GCF(342,348) = 6
LCM(342,348) = ( 342 × 348) / 6
LCM(342,348) = 119016 / 6
LCM(342,348) = 19836

1. What is the LCM of 342 and 348?

The LCM of 342 and 348 is 19836.

2. How to find the lowest common multiple of 342 and 348?

To find the lowest common multiple of 342 and 348, we have to get the multip;es of both numbers and identify the least common multiple in them which is 19836.

3. 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.

4. What are the Factors of 348?

Answer: Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348. There are 12 integers that are factors of 348. The greatest factor of 348 is 348.

Answer:

Least Common Multiple of 342 and 348 = 19836

Step 1: Find the prime factorization of 342

342 = 2 x 3 x 3 x 19

Step 2: Find the prime factorization of 348

348 = 2 x 2 x 3 x 29

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

LCM = 19836 = 2 x 2 x 3 x 3 x 19 x 29

Step 4: Therefore, the least common multiple of 342 and 348 is 19836.