Given Numbers are 384, 392

We can find the LCM of 384, 392 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 384 and 392

Multiples of 384 =384,768,1152,1536,1920,2304,2688,3072,3456,3840,4224,4608,4992,5376,5760,6144,6528,

Multiples of 392 =392,784,1176,1568,1960,2352,2744,3136,3528,3920,4312,4704,5096,5488,5880,6272,6664,

Now, get the least common multiple of 384, 392 which is 18816

So, the LCM of 384, 392 is 18816.

One method for determining the LCM of 384 and 392 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 384's prime factorization:

Prime factors of 384 are 2,3.

384 = 2⁷×3¹

And this is 392's prime factorization:

Prime factors of 392 are 2,7.

392 = 2³×7²

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

2⁷×3¹×7² = 18816

This shows that the LCM of 384 and 392 is 18816.

The first step in determining the Least Common Multiple of 384 and 392 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 384 and 392:

Lets look at the first ten multiples of these numbers, 384 and 392:

384,768,1152,1536,1920,2304,2688,3072,3456,6528 are the first ten multiples of 384.

392,784,1176,1568,1960,2352,2744,3136,3528,6664 are the first ten multiples of 392.

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 384 and 392, for example, are 4608, 6528, and 6272. 18816 is the least common multiple since it is the smallest.

384 and 392 have an LCM of 18816.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 384 and 392, than apply into the LCM equation.

GCF(384,392) = 8
LCM(384,392) = ( 384 × 392) / 8
LCM(384,392) = 150528 / 8
LCM(384,392) = 18816

1. What is the LCM of 384 and 392?

The LCM of 384 and 392 is 18816.

2. How to find the lowest common multiple of 384 and 392?

To find the lowest common multiple of 384 and 392, we have to get the multip;es of both numbers and identify the least common multiple in them which is 18816.

3. What are the Factors of 384?

Answer: Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. There are 16 integers that are factors of 384. The greatest factor of 384 is 384.

4. What are the Factors of 392?

Answer: Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. There are 12 integers that are factors of 392. The greatest factor of 392 is 392.

Answer:

Least Common Multiple of 384 and 392 = 18816

Step 1: Find the prime factorization of 384

384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 392

392 = 2 x 2 x 2 x 7 x 7

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

LCM = 18816 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 384 and 392 is 18816.