Given Numbers are 409, 415

We can find the LCM of 409, 415 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 409 and 415

Multiples of 409 =409,818,1227,1636,2045,2454,2863,3272,3681,4090,4499,4908,5317,5726,6135,6544,6953,

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 409, 415 which is 169735

So, the LCM of 409, 415 is 169735.

One method for determining the LCM of 409 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 409's prime factorization:

Prime factors of 409 are 409.

409 = 409¹

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:409, 5,83

5¹×83¹×409¹ = 169735

This shows that the LCM of 409 and 415 is 169735.

The first step in determining the Least Common Multiple of 409 and 415 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 409 and 415:

Lets look at the first ten multiples of these numbers, 409 and 415:

409,818,1227,1636,2045,2454,2863,3272,3681,6953 are the first ten multiples of 409.

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 409 and 415, for example, are 4908, 6953, and 6640. 169735 is the least common multiple since it is the smallest.

409 and 415 have an LCM of 169735.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 409 and 415, than apply into the LCM equation.

GCF(409,415) = 1
LCM(409,415) = ( 409 × 415) / 1
LCM(409,415) = 169735 / 1
LCM(409,415) = 169735

1. What is the LCM of 409 and 415?

The LCM of 409 and 415 is 169735.

2. How to find the lowest common multiple of 409 and 415?

To find the lowest common multiple of 409 and 415, we have to get the multip;es of both numbers and identify the least common multiple in them which is 169735.

3. What are the Factors of 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

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 409 and 415 = 169735

Step 1: Find the prime factorization of 409

409 = 409

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 = 169735 = 5 x 83 x 409

Step 4: Therefore, the least common multiple of 409 and 415 is 169735.