Given Numbers are 278, 284

We can find the LCM of 278, 284 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 278 and 284

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

Multiples of 284 =284,568,852,1136,1420,1704,1988,2272,2556,2840,3124,3408,3692,3976,4260,4544,4828,

Now, get the least common multiple of 278, 284 which is 39476

So, the LCM of 278, 284 is 39476.

One method for determining the LCM of 278 and 284 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 278's prime factorization:

Prime factors of 278 are 2,139.

278 = 2¹×139¹

And this is 284's prime factorization:

Prime factors of 284 are 2,71.

284 = 2²×71¹

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: 2,139,71

2²×71¹×139¹ = 39476

This shows that the LCM of 278 and 284 is 39476.

The first step in determining the Least Common Multiple of 278 and 284 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 278 and 284:

Lets look at the first ten multiples of these numbers, 278 and 284:

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

284,568,852,1136,1420,1704,1988,2272,2556,4828 are the first ten multiples of 284.

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 278 and 284, for example, are 3336, 4726, and 4544. 39476 is the least common multiple since it is the smallest.

278 and 284 have an LCM of 39476.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 278 and 284, than apply into the LCM equation.

GCF(278,284) = 2
LCM(278,284) = ( 278 × 284) / 2
LCM(278,284) = 78952 / 2
LCM(278,284) = 39476

1. What is the LCM of 278 and 284?

The LCM of 278 and 284 is 39476.

2. How to find the lowest common multiple of 278 and 284?

To find the lowest common multiple of 278 and 284, we have to get the multip;es of both numbers and identify the least common multiple in them which is 39476.

3. 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.

4. What are the Factors of 284?

Answer: Factors of 284 are 1, 2, 4, 71, 142, 284. There are 6 integers that are factors of 284. The greatest factor of 284 is 284.

Answer:

Least Common Multiple of 278 and 284 = 39476

Step 1: Find the prime factorization of 278

278 = 2 x 139

Step 2: Find the prime factorization of 284

284 = 2 x 2 x 71

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

LCM = 39476 = 2 x 2 x 71 x 139

Step 4: Therefore, the least common multiple of 278 and 284 is 39476.