Given Numbers are 288, 296

We can find the LCM of 288, 296 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 288 and 296

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

Multiples of 296 =296,592,888,1184,1480,1776,2072,2368,2664,2960,3256,3552,3848,4144,4440,4736,5032,

Now, get the least common multiple of 288, 296 which is 10656

So, the LCM of 288, 296 is 10656.

One method for determining the LCM of 288 and 296 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 296's prime factorization:

Prime factors of 296 are 2,37.

296 = 2³×37¹

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: 2,3,37

2⁵×3²×37¹ = 10656

This shows that the LCM of 288 and 296 is 10656.

The first step in determining the Least Common Multiple of 288 and 296 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 288 and 296:

Lets look at the first ten multiples of these numbers, 288 and 296:

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

296,592,888,1184,1480,1776,2072,2368,2664,5032 are the first ten multiples of 296.

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 296, for example, are 3456, 4896, and 4736. 10656 is the least common multiple since it is the smallest.

288 and 296 have an LCM of 10656.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 288 and 296, than apply into the LCM equation.

GCF(288,296) = 8
LCM(288,296) = ( 288 × 296) / 8
LCM(288,296) = 85248 / 8
LCM(288,296) = 10656

1. What is the LCM of 288 and 296?

The LCM of 288 and 296 is 10656.

2. How to find the lowest common multiple of 288 and 296?

To find the lowest common multiple of 288 and 296, we have to get the multip;es of both numbers and identify the least common multiple in them which is 10656.

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 296?

Answer: Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296. There are 8 integers that are factors of 296. The greatest factor of 296 is 296.

Answer:

Least Common Multiple of 288 and 296 = 10656

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 296

296 = 2 x 2 x 2 x 37

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

LCM = 10656 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 37

Step 4: Therefore, the least common multiple of 288 and 296 is 10656.