Given Numbers are 415, 419

We can find the LCM of 415, 419 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 415 and 419

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

Multiples of 419 =419,838,1257,1676,2095,2514,2933,3352,3771,4190,4609,5028,5447,5866,6285,6704,7123,

Now, get the least common multiple of 415, 419 which is 173885

So, the LCM of 415, 419 is 173885.

One method for determining the LCM of 415 and 419 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 415's prime factorization:

Prime factors of 415 are 5,83.

415 = 5¹×83¹

And this is 419's prime factorization:

Prime factors of 419 are 419.

419 = 419¹

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: 5,83,419

5¹×83¹×419¹ = 173885

This shows that the LCM of 415 and 419 is 173885.

The first step in determining the Least Common Multiple of 415 and 419 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 415 and 419:

Lets look at the first ten multiples of these numbers, 415 and 419:

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

419,838,1257,1676,2095,2514,2933,3352,3771,7123 are the first ten multiples of 419.

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 415 and 419, for example, are 4980, 7055, and 6704. 173885 is the least common multiple since it is the smallest.

415 and 419 have an LCM of 173885.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 415 and 419, than apply into the LCM equation.

GCF(415,419) = 1
LCM(415,419) = ( 415 × 419) / 1
LCM(415,419) = 173885 / 1
LCM(415,419) = 173885

1. What is the LCM of 415 and 419?

The LCM of 415 and 419 is 173885.

2. How to find the lowest common multiple of 415 and 419?

To find the lowest common multiple of 415 and 419, we have to get the multip;es of both numbers and identify the least common multiple in them which is 173885.

3. 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.

4. What are the Factors of 419?

Answer: Factors of 419 are 1, 419. There are 2 integers that are factors of 419. The greatest factor of 419 is 419.

Answer:

Least Common Multiple of 415 and 419 = 173885

Step 1: Find the prime factorization of 415

415 = 5 x 83

Step 2: Find the prime factorization of 419

419 = 419

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

LCM = 173885 = 5 x 83 x 419

Step 4: Therefore, the least common multiple of 415 and 419 is 173885.