Given Numbers are 460, 467

We can find the LCM of 460, 467 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 460 and 467

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

Multiples of 467 =467,934,1401,1868,2335,2802,3269,3736,4203,4670,5137,5604,6071,6538,7005,7472,7939,

Now, get the least common multiple of 460, 467 which is 214820

So, the LCM of 460, 467 is 214820.

One method for determining the LCM of 460 and 467 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 467's prime factorization:

Prime factors of 467 are 467.

467 = 467¹

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, 5,23,467

2²×5¹×23¹×467¹ = 214820

This shows that the LCM of 460 and 467 is 214820.

The first step in determining the Least Common Multiple of 460 and 467 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 460 and 467:

Lets look at the first ten multiples of these numbers, 460 and 467:

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

467,934,1401,1868,2335,2802,3269,3736,4203,7939 are the first ten multiples of 467.

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 467, for example, are 5520, 7820, and 7472. 214820 is the least common multiple since it is the smallest.

460 and 467 have an LCM of 214820.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 460 and 467, than apply into the LCM equation.

GCF(460,467) = 1
LCM(460,467) = ( 460 × 467) / 1
LCM(460,467) = 214820 / 1
LCM(460,467) = 214820

1. What is the LCM of 460 and 467?

The LCM of 460 and 467 is 214820.

2. How to find the lowest common multiple of 460 and 467?

To find the lowest common multiple of 460 and 467, we have to get the multip;es of both numbers and identify the least common multiple in them which is 214820.

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 467?

Answer: Factors of 467 are 1, 467. There are 2 integers that are factors of 467. The greatest factor of 467 is 467.

Answer:

Least Common Multiple of 460 and 467 = 214820

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 467

467 = 467

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

LCM = 214820 = 2 x 2 x 5 x 23 x 467

Step 4: Therefore, the least common multiple of 460 and 467 is 214820.