Given Numbers are 288, 292

We can find the LCM of 288, 292 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 288 and 292

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

Multiples of 292 =292,584,876,1168,1460,1752,2044,2336,2628,2920,3212,3504,3796,4088,4380,4672,4964,

Now, get the least common multiple of 288, 292 which is 21024

So, the LCM of 288, 292 is 21024.

One method for determining the LCM of 288 and 292 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 292's prime factorization:

Prime factors of 292 are 2,73.

292 = 2²×73¹

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: 2,3,73

2⁵×3²×73¹ = 21024

This shows that the LCM of 288 and 292 is 21024.

The first step in determining the Least Common Multiple of 288 and 292 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 288 and 292:

Lets look at the first ten multiples of these numbers, 288 and 292:

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

292,584,876,1168,1460,1752,2044,2336,2628,4964 are the first ten multiples of 292.

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 292, for example, are 3456, 4896, and 4672. 21024 is the least common multiple since it is the smallest.

288 and 292 have an LCM of 21024.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 288 and 292, than apply into the LCM equation.

GCF(288,292) = 4
LCM(288,292) = ( 288 × 292) / 4
LCM(288,292) = 84096 / 4
LCM(288,292) = 21024

1. What is the LCM of 288 and 292?

The LCM of 288 and 292 is 21024.

2. How to find the lowest common multiple of 288 and 292?

To find the lowest common multiple of 288 and 292, we have to get the multip;es of both numbers and identify the least common multiple in them which is 21024.

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 292?

Answer: Factors of 292 are 1, 2, 4, 73, 146, 292. There are 6 integers that are factors of 292. The greatest factor of 292 is 292.

Answer:

Least Common Multiple of 288 and 292 = 21024

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 292

292 = 2 x 2 x 73

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

LCM = 21024 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 73

Step 4: Therefore, the least common multiple of 288 and 292 is 21024.