Given Numbers are 260, 268

We can find the LCM of 260, 268 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 260 and 268

Multiples of 260 =260,520,780,1040,1300,1560,1820,2080,2340,2600,2860,3120,3380,3640,3900,4160,4420,

Multiples of 268 =268,536,804,1072,1340,1608,1876,2144,2412,2680,2948,3216,3484,3752,4020,4288,4556,

Now, get the least common multiple of 260, 268 which is 17420

So, the LCM of 260, 268 is 17420.

One method for determining the LCM of 260 and 268 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 260's prime factorization:

Prime factors of 260 are 2, 5,13.

260 = 2²×5¹×13¹

And this is 268's prime factorization:

Prime factors of 268 are 2,67.

268 = 2²×67¹

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, 5,13,67

2²×5¹×13¹×67¹ = 17420

This shows that the LCM of 260 and 268 is 17420.

The first step in determining the Least Common Multiple of 260 and 268 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 260 and 268:

Lets look at the first ten multiples of these numbers, 260 and 268:

260,520,780,1040,1300,1560,1820,2080,2340,4420 are the first ten multiples of 260.

268,536,804,1072,1340,1608,1876,2144,2412,4556 are the first ten multiples of 268.

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 260 and 268, for example, are 3120, 4420, and 4288. 17420 is the least common multiple since it is the smallest.

260 and 268 have an LCM of 17420.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 260 and 268, than apply into the LCM equation.

GCF(260,268) = 4
LCM(260,268) = ( 260 × 268) / 4
LCM(260,268) = 69680 / 4
LCM(260,268) = 17420

1. What is the LCM of 260 and 268?

The LCM of 260 and 268 is 17420.

2. How to find the lowest common multiple of 260 and 268?

To find the lowest common multiple of 260 and 268, we have to get the multip;es of both numbers and identify the least common multiple in them which is 17420.

3. What are the Factors of 260?

Answer: Factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260. There are 12 integers that are factors of 260. The greatest factor of 260 is 260.

4. What are the Factors of 268?

Answer: Factors of 268 are 1, 2, 4, 67, 134, 268. There are 6 integers that are factors of 268. The greatest factor of 268 is 268.

Answer:

Least Common Multiple of 260 and 268 = 17420

Step 1: Find the prime factorization of 260

260 = 2 x 2 x 5 x 13

Step 2: Find the prime factorization of 268

268 = 2 x 2 x 67

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

LCM = 17420 = 2 x 2 x 5 x 13 x 67

Step 4: Therefore, the least common multiple of 260 and 268 is 17420.