Given Numbers are 363, 368

We can find the LCM of 363, 368 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 363 and 368

Multiples of 363 =363,726,1089,1452,1815,2178,2541,2904,3267,3630,3993,4356,4719,5082,5445,5808,6171,

Multiples of 368 =368,736,1104,1472,1840,2208,2576,2944,3312,3680,4048,4416,4784,5152,5520,5888,6256,

Now, get the least common multiple of 363, 368 which is 133584

So, the LCM of 363, 368 is 133584.

One method for determining the LCM of 363 and 368 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 363's prime factorization:

Prime factors of 363 are 3,11.

363 = 3¹×11²

And this is 368's prime factorization:

Prime factors of 368 are 2,23.

368 = 2⁴×23¹

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: 3,11, 2,23

2⁴×3¹×11²×23¹ = 133584

This shows that the LCM of 363 and 368 is 133584.

The first step in determining the Least Common Multiple of 363 and 368 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 363 and 368:

Lets look at the first ten multiples of these numbers, 363 and 368:

363,726,1089,1452,1815,2178,2541,2904,3267,6171 are the first ten multiples of 363.

368,736,1104,1472,1840,2208,2576,2944,3312,6256 are the first ten multiples of 368.

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 363 and 368, for example, are 4356, 6171, and 5888. 133584 is the least common multiple since it is the smallest.

363 and 368 have an LCM of 133584.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 363 and 368, than apply into the LCM equation.

GCF(363,368) = 1
LCM(363,368) = ( 363 × 368) / 1
LCM(363,368) = 133584 / 1
LCM(363,368) = 133584

1. What is the LCM of 363 and 368?

The LCM of 363 and 368 is 133584.

2. How to find the lowest common multiple of 363 and 368?

To find the lowest common multiple of 363 and 368, we have to get the multip;es of both numbers and identify the least common multiple in them which is 133584.

3. What are the Factors of 363?

Answer: Factors of 363 are 1, 3, 11, 33, 121, 363. There are 6 integers that are factors of 363. The greatest factor of 363 is 363.

4. What are the Factors of 368?

Answer: Factors of 368 are 1, 2, 4, 8, 16, 23, 46, 92, 184, 368. There are 10 integers that are factors of 368. The greatest factor of 368 is 368.

Answer:

Least Common Multiple of 363 and 368 = 133584

Step 1: Find the prime factorization of 363

363 = 3 x 11 x 11

Step 2: Find the prime factorization of 368

368 = 2 x 2 x 2 x 2 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 = 133584 = 2 x 2 x 2 x 2 x 3 x 11 x 11 x 23

Step 4: Therefore, the least common multiple of 363 and 368 is 133584.