Given Numbers are 256, 262

We can find the LCM of 256, 262 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 256 and 262

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

Multiples of 262 =262,524,786,1048,1310,1572,1834,2096,2358,2620,2882,3144,3406,3668,3930,4192,4454,

Now, get the least common multiple of 256, 262 which is 33536

So, the LCM of 256, 262 is 33536.

One method for determining the LCM of 256 and 262 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 262's prime factorization:

Prime factors of 262 are 2,131.

262 = 2¹×131¹

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:2,131

2⁸×131¹ = 33536

This shows that the LCM of 256 and 262 is 33536.

The first step in determining the Least Common Multiple of 256 and 262 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 256 and 262:

Lets look at the first ten multiples of these numbers, 256 and 262:

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

262,524,786,1048,1310,1572,1834,2096,2358,4454 are the first ten multiples of 262.

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 262, for example, are 3072, 4352, and 4192. 33536 is the least common multiple since it is the smallest.

256 and 262 have an LCM of 33536.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 256 and 262, than apply into the LCM equation.

GCF(256,262) = 2
LCM(256,262) = ( 256 × 262) / 2
LCM(256,262) = 67072 / 2
LCM(256,262) = 33536

1. What is the LCM of 256 and 262?

The LCM of 256 and 262 is 33536.

2. How to find the lowest common multiple of 256 and 262?

To find the lowest common multiple of 256 and 262, we have to get the multip;es of both numbers and identify the least common multiple in them which is 33536.

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 262?

Answer: Factors of 262 are 1, 2, 131, 262. There are 4 integers that are factors of 262. The greatest factor of 262 is 262.

Answer:

Least Common Multiple of 256 and 262 = 33536

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 262

262 = 2 x 131

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

LCM = 33536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 131

Step 4: Therefore, the least common multiple of 256 and 262 is 33536.