Given Numbers are 224, 232

We can find the LCM of 224, 232 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 224 and 232

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

Multiples of 232 =232,464,696,928,1160,1392,1624,1856,2088,2320,2552,2784,3016,3248,3480,3712,3944,

Now, get the least common multiple of 224, 232 which is 6496

So, the LCM of 224, 232 is 6496.

One method for determining the LCM of 224 and 232 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 232's prime factorization:

Prime factors of 232 are 2,29.

232 = 2³×29¹

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: 2,7,29

2⁵×7¹×29¹ = 6496

This shows that the LCM of 224 and 232 is 6496.

The first step in determining the Least Common Multiple of 224 and 232 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 224 and 232:

Lets look at the first ten multiples of these numbers, 224 and 232:

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

232,464,696,928,1160,1392,1624,1856,2088,3944 are the first ten multiples of 232.

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 232, for example, are 2688, 3808, and 3712. 6496 is the least common multiple since it is the smallest.

224 and 232 have an LCM of 6496.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 224 and 232, than apply into the LCM equation.

GCF(224,232) = 8
LCM(224,232) = ( 224 × 232) / 8
LCM(224,232) = 51968 / 8
LCM(224,232) = 6496

1. What is the LCM of 224 and 232?

The LCM of 224 and 232 is 6496.

2. How to find the lowest common multiple of 224 and 232?

To find the lowest common multiple of 224 and 232, we have to get the multip;es of both numbers and identify the least common multiple in them which is 6496.

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 232?

Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.

Answer:

Least Common Multiple of 224 and 232 = 6496

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 232

232 = 2 x 2 x 2 x 29

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

LCM = 6496 = 2 x 2 x 2 x 2 x 2 x 7 x 29

Step 4: Therefore, the least common multiple of 224 and 232 is 6496.