Given Numbers are 460, 468

We can find the LCM of 460, 468 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 460 and 468

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

Multiples of 468 =468,936,1404,1872,2340,2808,3276,3744,4212,4680,5148,5616,6084,6552,7020,7488,7956,

Now, get the least common multiple of 460, 468 which is 53820

So, the LCM of 460, 468 is 53820.

One method for determining the LCM of 460 and 468 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 468's prime factorization:

Prime factors of 468 are 2, 3,13.

468 = 2²×3²×13¹

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, 3,13

2²×3²×5¹×13¹×23¹ = 53820

This shows that the LCM of 460 and 468 is 53820.

The first step in determining the Least Common Multiple of 460 and 468 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 460 and 468:

Lets look at the first ten multiples of these numbers, 460 and 468:

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

468,936,1404,1872,2340,2808,3276,3744,4212,7956 are the first ten multiples of 468.

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 468, for example, are 5520, 7820, and 7488. 53820 is the least common multiple since it is the smallest.

460 and 468 have an LCM of 53820.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 460 and 468, than apply into the LCM equation.

GCF(460,468) = 4
LCM(460,468) = ( 460 × 468) / 4
LCM(460,468) = 215280 / 4
LCM(460,468) = 53820

1. What is the LCM of 460 and 468?

The LCM of 460 and 468 is 53820.

2. How to find the lowest common multiple of 460 and 468?

To find the lowest common multiple of 460 and 468, we have to get the multip;es of both numbers and identify the least common multiple in them which is 53820.

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 468?

Answer: Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468. There are 18 integers that are factors of 468. The greatest factor of 468 is 468.

Answer:

Least Common Multiple of 460 and 468 = 53820

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 468

468 = 2 x 2 x 3 x 3 x 13

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

LCM = 53820 = 2 x 2 x 3 x 3 x 5 x 13 x 23

Step 4: Therefore, the least common multiple of 460 and 468 is 53820.