Given Numbers are 274, 278

We can find the LCM of 274, 278 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 274 and 278

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

Multiples of 278 =278,556,834,1112,1390,1668,1946,2224,2502,2780,3058,3336,3614,3892,4170,4448,4726,

Now, get the least common multiple of 274, 278 which is 38086

So, the LCM of 274, 278 is 38086.

One method for determining the LCM of 274 and 278 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 274's prime factorization:

Prime factors of 274 are 2,137.

274 = 2¹×137¹

And this is 278's prime factorization:

Prime factors of 278 are 2,139.

278 = 2¹×139¹

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: 2,137,139

2¹×137¹×139¹ = 38086

This shows that the LCM of 274 and 278 is 38086.

The first step in determining the Least Common Multiple of 274 and 278 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 274 and 278:

Lets look at the first ten multiples of these numbers, 274 and 278:

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

278,556,834,1112,1390,1668,1946,2224,2502,4726 are the first ten multiples of 278.

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 274 and 278, for example, are 3288, 4658, and 4448. 38086 is the least common multiple since it is the smallest.

274 and 278 have an LCM of 38086.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 274 and 278, than apply into the LCM equation.

GCF(274,278) = 2
LCM(274,278) = ( 274 × 278) / 2
LCM(274,278) = 76172 / 2
LCM(274,278) = 38086

1. What is the LCM of 274 and 278?

The LCM of 274 and 278 is 38086.

2. How to find the lowest common multiple of 274 and 278?

To find the lowest common multiple of 274 and 278, we have to get the multip;es of both numbers and identify the least common multiple in them which is 38086.

3. 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.

4. What are the Factors of 278?

Answer: Factors of 278 are 1, 2, 139, 278. There are 4 integers that are factors of 278. The greatest factor of 278 is 278.

Answer:

Least Common Multiple of 274 and 278 = 38086

Step 1: Find the prime factorization of 274

274 = 2 x 137

Step 2: Find the prime factorization of 278

278 = 2 x 139

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

LCM = 38086 = 2 x 137 x 139

Step 4: Therefore, the least common multiple of 274 and 278 is 38086.