Given Numbers are 257, 263

We can find the LCM of 257, 263 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 257 and 263

Multiples of 257 =257,514,771,1028,1285,1542,1799,2056,2313,2570,2827,3084,3341,3598,3855,4112,4369,

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 257, 263 which is 67591

So, the LCM of 257, 263 is 67591.

One method for determining the LCM of 257 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 257's prime factorization:

Prime factors of 257 are 257.

257 = 257¹

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:257,263

257¹×263¹ = 67591

This shows that the LCM of 257 and 263 is 67591.

The first step in determining the Least Common Multiple of 257 and 263 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 257 and 263:

Lets look at the first ten multiples of these numbers, 257 and 263:

257,514,771,1028,1285,1542,1799,2056,2313,4369 are the first ten multiples of 257.

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 257 and 263, for example, are 3084, 4369, and 4208. 67591 is the least common multiple since it is the smallest.

257 and 263 have an LCM of 67591.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 257 and 263, than apply into the LCM equation.

GCF(257,263) = 1
LCM(257,263) = ( 257 × 263) / 1
LCM(257,263) = 67591 / 1
LCM(257,263) = 67591

1. What is the LCM of 257 and 263?

The LCM of 257 and 263 is 67591.

2. How to find the lowest common multiple of 257 and 263?

To find the lowest common multiple of 257 and 263, we have to get the multip;es of both numbers and identify the least common multiple in them which is 67591.

3. What are the Factors of 257?

Answer: Factors of 257 are 1, 257. There are 2 integers that are factors of 257. The greatest factor of 257 is 257.

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 257 and 263 = 67591

Step 1: Find the prime factorization of 257

257 = 257

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 = 67591 = 257 x 263

Step 4: Therefore, the least common multiple of 257 and 263 is 67591.