Given Numbers are 288, 294

We can find the LCM of 288, 294 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 288 and 294

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

Multiples of 294 =294,588,882,1176,1470,1764,2058,2352,2646,2940,3234,3528,3822,4116,4410,4704,4998,

Now, get the least common multiple of 288, 294 which is 14112

So, the LCM of 288, 294 is 14112.

One method for determining the LCM of 288 and 294 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 294's prime factorization:

Prime factors of 294 are 2, 3,7.

294 = 2¹×3¹×7²

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: 2,3,7

2⁵×3²×7² = 14112

This shows that the LCM of 288 and 294 is 14112.

The first step in determining the Least Common Multiple of 288 and 294 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 288 and 294:

Lets look at the first ten multiples of these numbers, 288 and 294:

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

294,588,882,1176,1470,1764,2058,2352,2646,4998 are the first ten multiples of 294.

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 294, for example, are 3456, 4896, and 4704. 14112 is the least common multiple since it is the smallest.

288 and 294 have an LCM of 14112.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 288 and 294, than apply into the LCM equation.

GCF(288,294) = 6
LCM(288,294) = ( 288 × 294) / 6
LCM(288,294) = 84672 / 6
LCM(288,294) = 14112

1. What is the LCM of 288 and 294?

The LCM of 288 and 294 is 14112.

2. How to find the lowest common multiple of 288 and 294?

To find the lowest common multiple of 288 and 294, we have to get the multip;es of both numbers and identify the least common multiple in them which is 14112.

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 294?

Answer: Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294. There are 12 integers that are factors of 294. The greatest factor of 294 is 294.

Answer:

Least Common Multiple of 288 and 294 = 14112

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 294

294 = 2 x 3 x 7 x 7

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

LCM = 14112 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 288 and 294 is 14112.