Given Numbers are 268, 274

We can find the LCM of 268, 274 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 268 and 274

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

Multiples of 274 =274,548,822,1096,1370,1644,1918,2192,2466,2740,3014,3288,3562,3836,4110,4384,4658,

Now, get the least common multiple of 268, 274 which is 36716

So, the LCM of 268, 274 is 36716.

One method for determining the LCM of 268 and 274 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 268's prime factorization:

Prime factors of 268 are 2,67.

268 = 2²×67¹

And this is 274's prime factorization:

Prime factors of 274 are 2,137.

274 = 2¹×137¹

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: 2,67,137

2²×67¹×137¹ = 36716

This shows that the LCM of 268 and 274 is 36716.

The first step in determining the Least Common Multiple of 268 and 274 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 268 and 274:

Lets look at the first ten multiples of these numbers, 268 and 274:

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

274,548,822,1096,1370,1644,1918,2192,2466,4658 are the first ten multiples of 274.

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 268 and 274, for example, are 3216, 4556, and 4384. 36716 is the least common multiple since it is the smallest.

268 and 274 have an LCM of 36716.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 268 and 274, than apply into the LCM equation.

GCF(268,274) = 2
LCM(268,274) = ( 268 × 274) / 2
LCM(268,274) = 73432 / 2
LCM(268,274) = 36716

1. What is the LCM of 268 and 274?

The LCM of 268 and 274 is 36716.

2. How to find the lowest common multiple of 268 and 274?

To find the lowest common multiple of 268 and 274, we have to get the multip;es of both numbers and identify the least common multiple in them which is 36716.

3. 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.

4. What are the Factors of 274?

Answer: Factors of 274 are 1, 2, 137, 274. There are 4 integers that are factors of 274. The greatest factor of 274 is 274.

Answer:

Least Common Multiple of 268 and 274 = 36716

Step 1: Find the prime factorization of 268

268 = 2 x 2 x 67

Step 2: Find the prime factorization of 274

274 = 2 x 137

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

LCM = 36716 = 2 x 2 x 67 x 137

Step 4: Therefore, the least common multiple of 268 and 274 is 36716.