Given Numbers are 441, 448

We can find the LCM of 441, 448 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 441 and 448

Multiples of 441 =441,882,1323,1764,2205,2646,3087,3528,3969,4410,4851,5292,5733,6174,6615,7056,7497,

Multiples of 448 =448,896,1344,1792,2240,2688,3136,3584,4032,4480,4928,5376,5824,6272,6720,7168,7616,

Now, get the least common multiple of 441, 448 which is 28224

So, the LCM of 441, 448 is 28224.

One method for determining the LCM of 441 and 448 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 441's prime factorization:

Prime factors of 441 are 3,7.

441 = 3²×7²

And this is 448's prime factorization:

Prime factors of 448 are 2,7.

448 = 2⁶×7¹

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: 3,7,2

2⁶×3²×7² = 28224

This shows that the LCM of 441 and 448 is 28224.

The first step in determining the Least Common Multiple of 441 and 448 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 441 and 448:

Lets look at the first ten multiples of these numbers, 441 and 448:

441,882,1323,1764,2205,2646,3087,3528,3969,7497 are the first ten multiples of 441.

448,896,1344,1792,2240,2688,3136,3584,4032,7616 are the first ten multiples of 448.

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 441 and 448, for example, are 5292, 7497, and 7168. 28224 is the least common multiple since it is the smallest.

441 and 448 have an LCM of 28224.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 441 and 448, than apply into the LCM equation.

GCF(441,448) = 7
LCM(441,448) = ( 441 × 448) / 7
LCM(441,448) = 197568 / 7
LCM(441,448) = 28224

1. What is the LCM of 441 and 448?

The LCM of 441 and 448 is 28224.

2. How to find the lowest common multiple of 441 and 448?

To find the lowest common multiple of 441 and 448, we have to get the multip;es of both numbers and identify the least common multiple in them which is 28224.

3. What are the Factors of 441?

Answer: Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441. There are 9 integers that are factors of 441. The greatest factor of 441 is 441.

4. What are the Factors of 448?

Answer: Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. There are 14 integers that are factors of 448. The greatest factor of 448 is 448.

Answer:

Least Common Multiple of 441 and 448 = 28224

Step 1: Find the prime factorization of 441

441 = 3 x 3 x 7 x 7

Step 2: Find the prime factorization of 448

448 = 2 x 2 x 2 x 2 x 2 x 2 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 = 28224 = 2 x 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 441 and 448 is 28224.