Given Numbers are 280, 284

We can find the LCM of 280, 284 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 280 and 284

Multiples of 280 =280,560,840,1120,1400,1680,1960,2240,2520,2800,3080,3360,3640,3920,4200,4480,4760,

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 280, 284 which is 19880

So, the LCM of 280, 284 is 19880.

One method for determining the LCM of 280 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 280's prime factorization:

Prime factors of 280 are 2, 5,7.

280 = 2³×5¹×7¹

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, 5,7,71

2³×5¹×7¹×71¹ = 19880

This shows that the LCM of 280 and 284 is 19880.

The first step in determining the Least Common Multiple of 280 and 284 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 280 and 284:

Lets look at the first ten multiples of these numbers, 280 and 284:

280,560,840,1120,1400,1680,1960,2240,2520,4760 are the first ten multiples of 280.

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 280 and 284, for example, are 3360, 4760, and 4544. 19880 is the least common multiple since it is the smallest.

280 and 284 have an LCM of 19880.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 280 and 284, than apply into the LCM equation.

GCF(280,284) = 4
LCM(280,284) = ( 280 × 284) / 4
LCM(280,284) = 79520 / 4
LCM(280,284) = 19880

1. What is the LCM of 280 and 284?

The LCM of 280 and 284 is 19880.

2. How to find the lowest common multiple of 280 and 284?

To find the lowest common multiple of 280 and 284, we have to get the multip;es of both numbers and identify the least common multiple in them which is 19880.

3. What are the Factors of 280?

Answer: Factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. There are 16 integers that are factors of 280. The greatest factor of 280 is 280.

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 280 and 284 = 19880

Step 1: Find the prime factorization of 280

280 = 2 x 2 x 2 x 5 x 7

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 = 19880 = 2 x 2 x 2 x 5 x 7 x 71

Step 4: Therefore, the least common multiple of 280 and 284 is 19880.