Given Numbers are 460, 464

We can find the LCM of 460, 464 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 460 and 464

Multiples of 460 =460,920,1380,1840,2300,2760,3220,3680,4140,4600,5060,5520,5980,6440,6900,7360,7820,

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 460, 464 which is 53360

So, the LCM of 460, 464 is 53360.

One method for determining the LCM of 460 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 460's prime factorization:

Prime factors of 460 are 2, 5,23.

460 = 2²×5¹×23¹

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, 5,23,29

2⁴×5¹×23¹×29¹ = 53360

This shows that the LCM of 460 and 464 is 53360.

The first step in determining the Least Common Multiple of 460 and 464 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 460 and 464:

Lets look at the first ten multiples of these numbers, 460 and 464:

460,920,1380,1840,2300,2760,3220,3680,4140,7820 are the first ten multiples of 460.

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 460 and 464, for example, are 5520, 7820, and 7424. 53360 is the least common multiple since it is the smallest.

460 and 464 have an LCM of 53360.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 460 and 464, than apply into the LCM equation.

GCF(460,464) = 4
LCM(460,464) = ( 460 × 464) / 4
LCM(460,464) = 213440 / 4
LCM(460,464) = 53360

1. What is the LCM of 460 and 464?

The LCM of 460 and 464 is 53360.

2. How to find the lowest common multiple of 460 and 464?

To find the lowest common multiple of 460 and 464, we have to get the multip;es of both numbers and identify the least common multiple in them which is 53360.

3. What are the Factors of 460?

Answer: Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. There are 12 integers that are factors of 460. The greatest factor of 460 is 460.

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 460 and 464 = 53360

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

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 = 53360 = 2 x 2 x 2 x 2 x 5 x 23 x 29

Step 4: Therefore, the least common multiple of 460 and 464 is 53360.