Given Numbers are 408, 415

We can find the LCM of 408, 415 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 408 and 415

Multiples of 408 =408,816,1224,1632,2040,2448,2856,3264,3672,4080,4488,4896,5304,5712,6120,6528,6936,

Multiples of 415 =415,830,1245,1660,2075,2490,2905,3320,3735,4150,4565,4980,5395,5810,6225,6640,7055,

Now, get the least common multiple of 408, 415 which is 169320

So, the LCM of 408, 415 is 169320.

One method for determining the LCM of 408 and 415 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 408's prime factorization:

Prime factors of 408 are 2, 3,17.

408 = 2³×3¹×17¹

And this is 415's prime factorization:

Prime factors of 415 are 5,83.

415 = 5¹×83¹

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, 3,17, 5,83

2³×3¹×5¹×17¹×83¹ = 169320

This shows that the LCM of 408 and 415 is 169320.

The first step in determining the Least Common Multiple of 408 and 415 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 408 and 415:

Lets look at the first ten multiples of these numbers, 408 and 415:

408,816,1224,1632,2040,2448,2856,3264,3672,6936 are the first ten multiples of 408.

415,830,1245,1660,2075,2490,2905,3320,3735,7055 are the first ten multiples of 415.

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 408 and 415, for example, are 4896, 6936, and 6640. 169320 is the least common multiple since it is the smallest.

408 and 415 have an LCM of 169320.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 408 and 415, than apply into the LCM equation.

GCF(408,415) = 1
LCM(408,415) = ( 408 × 415) / 1
LCM(408,415) = 169320 / 1
LCM(408,415) = 169320

1. What is the LCM of 408 and 415?

The LCM of 408 and 415 is 169320.

2. How to find the lowest common multiple of 408 and 415?

To find the lowest common multiple of 408 and 415, we have to get the multip;es of both numbers and identify the least common multiple in them which is 169320.

3. What are the Factors of 408?

Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.

4. What are the Factors of 415?

Answer: Factors of 415 are 1, 5, 83, 415. There are 4 integers that are factors of 415. The greatest factor of 415 is 415.

Answer:

Least Common Multiple of 408 and 415 = 169320

Step 1: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

Step 2: Find the prime factorization of 415

415 = 5 x 83

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

LCM = 169320 = 2 x 2 x 2 x 3 x 5 x 17 x 83

Step 4: Therefore, the least common multiple of 408 and 415 is 169320.