Given Numbers are 448, 456

We can find the LCM of 448, 456 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 448 and 456

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

Multiples of 456 =456,912,1368,1824,2280,2736,3192,3648,4104,4560,5016,5472,5928,6384,6840,7296,7752,

Now, get the least common multiple of 448, 456 which is 25536

So, the LCM of 448, 456 is 25536.

One method for determining the LCM of 448 and 456 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 448's prime factorization:

Prime factors of 448 are 2,7.

448 = 2⁶×7¹

And this is 456's prime factorization:

Prime factors of 456 are 2, 3,19.

456 = 2³×3¹×19¹

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, 3,19

2⁶×3¹×7¹×19¹ = 25536

This shows that the LCM of 448 and 456 is 25536.

The first step in determining the Least Common Multiple of 448 and 456 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 448 and 456:

Lets look at the first ten multiples of these numbers, 448 and 456:

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

456,912,1368,1824,2280,2736,3192,3648,4104,7752 are the first ten multiples of 456.

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 448 and 456, for example, are 5376, 7616, and 7296. 25536 is the least common multiple since it is the smallest.

448 and 456 have an LCM of 25536.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 448 and 456, than apply into the LCM equation.

GCF(448,456) = 8
LCM(448,456) = ( 448 × 456) / 8
LCM(448,456) = 204288 / 8
LCM(448,456) = 25536

1. What is the LCM of 448 and 456?

The LCM of 448 and 456 is 25536.

2. How to find the lowest common multiple of 448 and 456?

To find the lowest common multiple of 448 and 456, we have to get the multip;es of both numbers and identify the least common multiple in them which is 25536.

3. 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.

4. What are the Factors of 456?

Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.

Answer:

Least Common Multiple of 448 and 456 = 25536

Step 1: Find the prime factorization of 448

448 = 2 x 2 x 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

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

LCM = 25536 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 448 and 456 is 25536.