Given Numbers are 257, 262

We can find the LCM of 257, 262 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 257 and 262

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

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 257, 262 which is 67334

So, the LCM of 257, 262 is 67334.

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

Prime factors of 257 are 257.

257 = 257¹

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:257, 2,131

2¹×131¹×257¹ = 67334

This shows that the LCM of 257 and 262 is 67334.

The first step in determining the Least Common Multiple of 257 and 262 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 257 and 262:

Lets look at the first ten multiples of these numbers, 257 and 262:

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

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 257 and 262, for example, are 3084, 4369, and 4192. 67334 is the least common multiple since it is the smallest.

257 and 262 have an LCM of 67334.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 257 and 262, than apply into the LCM equation.

GCF(257,262) = 1
LCM(257,262) = ( 257 × 262) / 1
LCM(257,262) = 67334 / 1
LCM(257,262) = 67334

1. What is the LCM of 257 and 262?

The LCM of 257 and 262 is 67334.

2. How to find the lowest common multiple of 257 and 262?

To find the lowest common multiple of 257 and 262, we have to get the multip;es of both numbers and identify the least common multiple in them which is 67334.

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 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 257 and 262 = 67334

Step 1: Find the prime factorization of 257

257 = 257

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 = 67334 = 2 x 131 x 257

Step 4: Therefore, the least common multiple of 257 and 262 is 67334.