Given Numbers are 266, 274

We can find the LCM of 266, 274 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 266 and 274

Multiples of 266 =266,532,798,1064,1330,1596,1862,2128,2394,2660,2926,3192,3458,3724,3990,4256,4522,

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 266, 274 which is 36442

So, the LCM of 266, 274 is 36442.

One method for determining the LCM of 266 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 266's prime factorization:

Prime factors of 266 are 2, 7,19.

266 = 2¹×7¹×19¹

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, 7,19,137

2¹×7¹×19¹×137¹ = 36442

This shows that the LCM of 266 and 274 is 36442.

The first step in determining the Least Common Multiple of 266 and 274 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 266 and 274:

Lets look at the first ten multiples of these numbers, 266 and 274:

266,532,798,1064,1330,1596,1862,2128,2394,4522 are the first ten multiples of 266.

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 266 and 274, for example, are 3192, 4522, and 4384. 36442 is the least common multiple since it is the smallest.

266 and 274 have an LCM of 36442.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 266 and 274, than apply into the LCM equation.

GCF(266,274) = 2
LCM(266,274) = ( 266 × 274) / 2
LCM(266,274) = 72884 / 2
LCM(266,274) = 36442

1. What is the LCM of 266 and 274?

The LCM of 266 and 274 is 36442.

2. How to find the lowest common multiple of 266 and 274?

To find the lowest common multiple of 266 and 274, we have to get the multip;es of both numbers and identify the least common multiple in them which is 36442.

3. What are the Factors of 266?

Answer: Factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266. There are 8 integers that are factors of 266. The greatest factor of 266 is 266.

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 266 and 274 = 36442

Step 1: Find the prime factorization of 266

266 = 2 x 7 x 19

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 = 36442 = 2 x 7 x 19 x 137

Step 4: Therefore, the least common multiple of 266 and 274 is 36442.