Given Numbers are 256, 261

We can find the LCM of 256, 261 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 256 and 261

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

Multiples of 261 =261,522,783,1044,1305,1566,1827,2088,2349,2610,2871,3132,3393,3654,3915,4176,4437,

Now, get the least common multiple of 256, 261 which is 66816

So, the LCM of 256, 261 is 66816.

One method for determining the LCM of 256 and 261 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 261's prime factorization:

Prime factors of 261 are 3,29.

261 = 3²×29¹

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, 3,29

2⁸×3²×29¹ = 66816

This shows that the LCM of 256 and 261 is 66816.

The first step in determining the Least Common Multiple of 256 and 261 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 256 and 261:

Lets look at the first ten multiples of these numbers, 256 and 261:

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

261,522,783,1044,1305,1566,1827,2088,2349,4437 are the first ten multiples of 261.

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 261, for example, are 3072, 4352, and 4176. 66816 is the least common multiple since it is the smallest.

256 and 261 have an LCM of 66816.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 256 and 261, than apply into the LCM equation.

GCF(256,261) = 1
LCM(256,261) = ( 256 × 261) / 1
LCM(256,261) = 66816 / 1
LCM(256,261) = 66816

1. What is the LCM of 256 and 261?

The LCM of 256 and 261 is 66816.

2. How to find the lowest common multiple of 256 and 261?

To find the lowest common multiple of 256 and 261, we have to get the multip;es of both numbers and identify the least common multiple in them which is 66816.

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 261?

Answer: Factors of 261 are 1, 3, 9, 29, 87, 261. There are 6 integers that are factors of 261. The greatest factor of 261 is 261.

Answer:

Least Common Multiple of 256 and 261 = 66816

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 261

261 = 3 x 3 x 29

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

LCM = 66816 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 29

Step 4: Therefore, the least common multiple of 256 and 261 is 66816.