Given Numbers are 456, 464

We can find the LCM of 456, 464 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 456 and 464

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

Multiples of 464 =464,928,1392,1856,2320,2784,3248,3712,4176,4640,5104,5568,6032,6496,6960,7424,7888,

Now, get the least common multiple of 456, 464 which is 26448

So, the LCM of 456, 464 is 26448.

One method for determining the LCM of 456 and 464 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 456's prime factorization:

Prime factors of 456 are 2, 3,19.

456 = 2³×3¹×19¹

And this is 464's prime factorization:

Prime factors of 464 are 2,29.

464 = 2⁴×29¹

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, 3,19,29

2⁴×3¹×19¹×29¹ = 26448

This shows that the LCM of 456 and 464 is 26448.

The first step in determining the Least Common Multiple of 456 and 464 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 456 and 464:

Lets look at the first ten multiples of these numbers, 456 and 464:

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

464,928,1392,1856,2320,2784,3248,3712,4176,7888 are the first ten multiples of 464.

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 456 and 464, for example, are 5472, 7752, and 7424. 26448 is the least common multiple since it is the smallest.

456 and 464 have an LCM of 26448.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 456 and 464, than apply into the LCM equation.

GCF(456,464) = 8
LCM(456,464) = ( 456 × 464) / 8
LCM(456,464) = 211584 / 8
LCM(456,464) = 26448

1. What is the LCM of 456 and 464?

The LCM of 456 and 464 is 26448.

2. How to find the lowest common multiple of 456 and 464?

To find the lowest common multiple of 456 and 464, we have to get the multip;es of both numbers and identify the least common multiple in them which is 26448.

3. 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.

4. What are the Factors of 464?

Answer: Factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464. There are 10 integers that are factors of 464. The greatest factor of 464 is 464.

Answer:

Least Common Multiple of 456 and 464 = 26448

Step 1: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

Step 2: Find the prime factorization of 464

464 = 2 x 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 = 26448 = 2 x 2 x 2 x 2 x 3 x 19 x 29

Step 4: Therefore, the least common multiple of 456 and 464 is 26448.