Given Numbers are 288, 293

We can find the LCM of 288, 293 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 288 and 293

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

Multiples of 293 =293,586,879,1172,1465,1758,2051,2344,2637,2930,3223,3516,3809,4102,4395,4688,4981,

Now, get the least common multiple of 288, 293 which is 84384

So, the LCM of 288, 293 is 84384.

One method for determining the LCM of 288 and 293 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 288's prime factorization:

Prime factors of 288 are 2,3.

288 = 2⁵×3²

And this is 293's prime factorization:

Prime factors of 293 are 293.

293 = 293¹

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: 2,3,293

2⁵×3²×293¹ = 84384

This shows that the LCM of 288 and 293 is 84384.

The first step in determining the Least Common Multiple of 288 and 293 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 288 and 293:

Lets look at the first ten multiples of these numbers, 288 and 293:

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

293,586,879,1172,1465,1758,2051,2344,2637,4981 are the first ten multiples of 293.

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 288 and 293, for example, are 3456, 4896, and 4688. 84384 is the least common multiple since it is the smallest.

288 and 293 have an LCM of 84384.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 288 and 293, than apply into the LCM equation.

GCF(288,293) = 1
LCM(288,293) = ( 288 × 293) / 1
LCM(288,293) = 84384 / 1
LCM(288,293) = 84384

1. What is the LCM of 288 and 293?

The LCM of 288 and 293 is 84384.

2. How to find the lowest common multiple of 288 and 293?

To find the lowest common multiple of 288 and 293, we have to get the multip;es of both numbers and identify the least common multiple in them which is 84384.

3. 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.

4. What are the Factors of 293?

Answer: Factors of 293 are 1, 293. There are 2 integers that are factors of 293. The greatest factor of 293 is 293.

Answer:

Least Common Multiple of 288 and 293 = 84384

Step 1: Find the prime factorization of 288

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

Step 2: Find the prime factorization of 293

293 = 293

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

LCM = 84384 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 293

Step 4: Therefore, the least common multiple of 288 and 293 is 84384.