Given Numbers are 336, 342

We can find the LCM of 336, 342 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 336 and 342

Multiples of 336 =336,672,1008,1344,1680,2016,2352,2688,3024,3360,3696,4032,4368,4704,5040,5376,5712,

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 336, 342 which is 19152

So, the LCM of 336, 342 is 19152.

One method for determining the LCM of 336 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 336's prime factorization:

Prime factors of 336 are 2, 3,7.

336 = 2⁴×3¹×7¹

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, 3,7,19

2⁴×3²×7¹×19¹ = 19152

This shows that the LCM of 336 and 342 is 19152.

The first step in determining the Least Common Multiple of 336 and 342 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 336 and 342:

Lets look at the first ten multiples of these numbers, 336 and 342:

336,672,1008,1344,1680,2016,2352,2688,3024,5712 are the first ten multiples of 336.

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 336 and 342, for example, are 4032, 5712, and 5472. 19152 is the least common multiple since it is the smallest.

336 and 342 have an LCM of 19152.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 336 and 342, than apply into the LCM equation.

GCF(336,342) = 6
LCM(336,342) = ( 336 × 342) / 6
LCM(336,342) = 114912 / 6
LCM(336,342) = 19152

1. What is the LCM of 336 and 342?

The LCM of 336 and 342 is 19152.

2. How to find the lowest common multiple of 336 and 342?

To find the lowest common multiple of 336 and 342, we have to get the multip;es of both numbers and identify the least common multiple in them which is 19152.

3. What are the Factors of 336?

Answer: Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336. There are 20 integers that are factors of 336. The greatest factor of 336 is 336.

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 336 and 342 = 19152

Step 1: Find the prime factorization of 336

336 = 2 x 2 x 2 x 2 x 3 x 7

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 = 19152 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 336 and 342 is 19152.