Given Numbers are 256, 263

We can find the LCM of 256, 263 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 256 and 263

Multiples of 256 =256,512,768,1024,1280,1536,1792,2048,2304,2560,2816,3072,3328,3584,3840,4096,4352,

Multiples of 263 =263,526,789,1052,1315,1578,1841,2104,2367,2630,2893,3156,3419,3682,3945,4208,4471,

Now, get the least common multiple of 256, 263 which is 67328

So, the LCM of 256, 263 is 67328.

One method for determining the LCM of 256 and 263 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 256's prime factorization:

Prime factors of 256 are 2.

256 = 2⁸

And this is 263's prime factorization:

Prime factors of 263 are 263.

263 = 263¹

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:2,263

2⁸×263¹ = 67328

This shows that the LCM of 256 and 263 is 67328.

The first step in determining the Least Common Multiple of 256 and 263 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 256 and 263:

Lets look at the first ten multiples of these numbers, 256 and 263:

256,512,768,1024,1280,1536,1792,2048,2304,4352 are the first ten multiples of 256.

263,526,789,1052,1315,1578,1841,2104,2367,4471 are the first ten multiples of 263.

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 256 and 263, for example, are 3072, 4352, and 4208. 67328 is the least common multiple since it is the smallest.

256 and 263 have an LCM of 67328.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 256 and 263, than apply into the LCM equation.

GCF(256,263) = 1
LCM(256,263) = ( 256 × 263) / 1
LCM(256,263) = 67328 / 1
LCM(256,263) = 67328

1. What is the LCM of 256 and 263?

The LCM of 256 and 263 is 67328.

2. How to find the lowest common multiple of 256 and 263?

To find the lowest common multiple of 256 and 263, we have to get the multip;es of both numbers and identify the least common multiple in them which is 67328.

3. What are the Factors of 256?

Answer: Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256. There are 9 integers that are factors of 256. The greatest factor of 256 is 256.

4. What are the Factors of 263?

Answer: Factors of 263 are 1, 263. There are 2 integers that are factors of 263. The greatest factor of 263 is 263.

Answer:

Least Common Multiple of 256 and 263 = 67328

Step 1: Find the prime factorization of 256

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 263

263 = 263

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

LCM = 67328 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 263

Step 4: Therefore, the least common multiple of 256 and 263 is 67328.