Given Numbers are 192, 199

We can find the LCM of 192, 199 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 192 and 199

Multiples of 192 =192,384,576,768,960,1152,1344,1536,1728,1920,2112,2304,2496,2688,2880,3072,3264,

Multiples of 199 =199,398,597,796,995,1194,1393,1592,1791,1990,2189,2388,2587,2786,2985,3184,3383,

Now, get the least common multiple of 192, 199 which is 38208

So, the LCM of 192, 199 is 38208.

One method for determining the LCM of 192 and 199 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 192's prime factorization:

Prime factors of 192 are 2,3.

192 = 2⁶×3¹

And this is 199's prime factorization:

Prime factors of 199 are 199.

199 = 199¹

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: 2,3,199

2⁶×3¹×199¹ = 38208

This shows that the LCM of 192 and 199 is 38208.

The first step in determining the Least Common Multiple of 192 and 199 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 192 and 199:

Lets look at the first ten multiples of these numbers, 192 and 199:

192,384,576,768,960,1152,1344,1536,1728,3264 are the first ten multiples of 192.

199,398,597,796,995,1194,1393,1592,1791,3383 are the first ten multiples of 199.

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 192 and 199, for example, are 2304, 3264, and 3184. 38208 is the least common multiple since it is the smallest.

192 and 199 have an LCM of 38208.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 192 and 199, than apply into the LCM equation.

GCF(192,199) = 1
LCM(192,199) = ( 192 × 199) / 1
LCM(192,199) = 38208 / 1
LCM(192,199) = 38208

1. What is the LCM of 192 and 199?

The LCM of 192 and 199 is 38208.

2. How to find the lowest common multiple of 192 and 199?

To find the lowest common multiple of 192 and 199, we have to get the multip;es of both numbers and identify the least common multiple in them which is 38208.

3. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

4. What are the Factors of 199?

Answer: Factors of 199 are 1, 199. There are 2 integers that are factors of 199. The greatest factor of 199 is 199.

Answer:

Least Common Multiple of 192 and 199 = 38208

Step 1: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 199

199 = 199

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

LCM = 38208 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 199

Step 4: Therefore, the least common multiple of 192 and 199 is 38208.