Given Numbers are 257, 265

We can find the LCM of 257, 265 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 257 and 265

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

Multiples of 265 =265,530,795,1060,1325,1590,1855,2120,2385,2650,2915,3180,3445,3710,3975,4240,4505,

Now, get the least common multiple of 257, 265 which is 68105

So, the LCM of 257, 265 is 68105.

One method for determining the LCM of 257 and 265 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 265's prime factorization:

Prime factors of 265 are 5,53.

265 = 5¹×53¹

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, 5,53

5¹×53¹×257¹ = 68105

This shows that the LCM of 257 and 265 is 68105.

The first step in determining the Least Common Multiple of 257 and 265 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 257 and 265:

Lets look at the first ten multiples of these numbers, 257 and 265:

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

265,530,795,1060,1325,1590,1855,2120,2385,4505 are the first ten multiples of 265.

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 265, for example, are 3084, 4369, and 4240. 68105 is the least common multiple since it is the smallest.

257 and 265 have an LCM of 68105.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 257 and 265, than apply into the LCM equation.

GCF(257,265) = 1
LCM(257,265) = ( 257 × 265) / 1
LCM(257,265) = 68105 / 1
LCM(257,265) = 68105

1. What is the LCM of 257 and 265?

The LCM of 257 and 265 is 68105.

2. How to find the lowest common multiple of 257 and 265?

To find the lowest common multiple of 257 and 265, we have to get the multip;es of both numbers and identify the least common multiple in them which is 68105.

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 265?

Answer: Factors of 265 are 1, 5, 53, 265. There are 4 integers that are factors of 265. The greatest factor of 265 is 265.

Answer:

Least Common Multiple of 257 and 265 = 68105

Step 1: Find the prime factorization of 257

257 = 257

Step 2: Find the prime factorization of 265

265 = 5 x 53

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

LCM = 68105 = 5 x 53 x 257

Step 4: Therefore, the least common multiple of 257 and 265 is 68105.