Given Numbers are 224, 231

We can find the LCM of 224, 231 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 224 and 231

Multiples of 224 =224,448,672,896,1120,1344,1568,1792,2016,2240,2464,2688,2912,3136,3360,3584,3808,

Multiples of 231 =231,462,693,924,1155,1386,1617,1848,2079,2310,2541,2772,3003,3234,3465,3696,3927,

Now, get the least common multiple of 224, 231 which is 7392

So, the LCM of 224, 231 is 7392.

One method for determining the LCM of 224 and 231 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 224's prime factorization:

Prime factors of 224 are 2,7.

224 = 2⁵×7¹

And this is 231's prime factorization:

Prime factors of 231 are 3, 7,11.

231 = 3¹×7¹×11¹

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: 2,7, 3,11

2⁵×3¹×7¹×11¹ = 7392

This shows that the LCM of 224 and 231 is 7392.

The first step in determining the Least Common Multiple of 224 and 231 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 224 and 231:

Lets look at the first ten multiples of these numbers, 224 and 231:

224,448,672,896,1120,1344,1568,1792,2016,3808 are the first ten multiples of 224.

231,462,693,924,1155,1386,1617,1848,2079,3927 are the first ten multiples of 231.

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 224 and 231, for example, are 2688, 3808, and 3696. 7392 is the least common multiple since it is the smallest.

224 and 231 have an LCM of 7392.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 224 and 231, than apply into the LCM equation.

GCF(224,231) = 7
LCM(224,231) = ( 224 × 231) / 7
LCM(224,231) = 51744 / 7
LCM(224,231) = 7392

1. What is the LCM of 224 and 231?

The LCM of 224 and 231 is 7392.

2. How to find the lowest common multiple of 224 and 231?

To find the lowest common multiple of 224 and 231, we have to get the multip;es of both numbers and identify the least common multiple in them which is 7392.

3. What are the Factors of 224?

Answer: Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. There are 12 integers that are factors of 224. The greatest factor of 224 is 224.

4. What are the Factors of 231?

Answer: Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. There are 8 integers that are factors of 231. The greatest factor of 231 is 231.

Answer:

Least Common Multiple of 224 and 231 = 7392

Step 1: Find the prime factorization of 224

224 = 2 x 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 231

231 = 3 x 7 x 11

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

LCM = 7392 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 224 and 231 is 7392.