Given Numbers are 409, 417

We can find the LCM of 409, 417 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 409 and 417

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

Multiples of 417 =417,834,1251,1668,2085,2502,2919,3336,3753,4170,4587,5004,5421,5838,6255,6672,7089,

Now, get the least common multiple of 409, 417 which is 170553

So, the LCM of 409, 417 is 170553.

One method for determining the LCM of 409 and 417 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 417's prime factorization:

Prime factors of 417 are 3,139.

417 = 3¹×139¹

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, 3,139

3¹×139¹×409¹ = 170553

This shows that the LCM of 409 and 417 is 170553.

The first step in determining the Least Common Multiple of 409 and 417 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 409 and 417:

Lets look at the first ten multiples of these numbers, 409 and 417:

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

417,834,1251,1668,2085,2502,2919,3336,3753,7089 are the first ten multiples of 417.

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 417, for example, are 4908, 6953, and 6672. 170553 is the least common multiple since it is the smallest.

409 and 417 have an LCM of 170553.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 409 and 417, than apply into the LCM equation.

GCF(409,417) = 1
LCM(409,417) = ( 409 × 417) / 1
LCM(409,417) = 170553 / 1
LCM(409,417) = 170553

1. What is the LCM of 409 and 417?

The LCM of 409 and 417 is 170553.

2. How to find the lowest common multiple of 409 and 417?

To find the lowest common multiple of 409 and 417, we have to get the multip;es of both numbers and identify the least common multiple in them which is 170553.

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 417?

Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.

Answer:

Least Common Multiple of 409 and 417 = 170553

Step 1: Find the prime factorization of 409

409 = 409

Step 2: Find the prime factorization of 417

417 = 3 x 139

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

LCM = 170553 = 3 x 139 x 409

Step 4: Therefore, the least common multiple of 409 and 417 is 170553.