Given Numbers are 280, 288

We can find the LCM of 280, 288 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 280 and 288

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

Multiples of 288 =288,576,864,1152,1440,1728,2016,2304,2592,2880,3168,3456,3744,4032,4320,4608,4896,

Now, get the least common multiple of 280, 288 which is 10080

So, the LCM of 280, 288 is 10080.

One method for determining the LCM of 280 and 288 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 288's prime factorization:

Prime factors of 288 are 2,3.

288 = 2⁵×3²

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, 5,7,3

2⁵×3²×5¹×7¹ = 10080

This shows that the LCM of 280 and 288 is 10080.

The first step in determining the Least Common Multiple of 280 and 288 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 280 and 288:

Lets look at the first ten multiples of these numbers, 280 and 288:

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

288,576,864,1152,1440,1728,2016,2304,2592,4896 are the first ten multiples of 288.

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 288, for example, are 3360, 4760, and 4608. 10080 is the least common multiple since it is the smallest.

280 and 288 have an LCM of 10080.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 280 and 288, than apply into the LCM equation.

GCF(280,288) = 8
LCM(280,288) = ( 280 × 288) / 8
LCM(280,288) = 80640 / 8
LCM(280,288) = 10080

1. What is the LCM of 280 and 288?

The LCM of 280 and 288 is 10080.

2. How to find the lowest common multiple of 280 and 288?

To find the lowest common multiple of 280 and 288, we have to get the multip;es of both numbers and identify the least common multiple in them which is 10080.

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 288?

Answer: Factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288. There are 18 integers that are factors of 288. The greatest factor of 288 is 288.

Answer:

Least Common Multiple of 280 and 288 = 10080

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 288

288 = 2 x 2 x 2 x 2 x 2 x 3 x 3

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

LCM = 10080 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 280 and 288 is 10080.