Given Numbers are 414, 419

We can find the LCM of 414, 419 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 414 and 419

Multiples of 414 =414,828,1242,1656,2070,2484,2898,3312,3726,4140,4554,4968,5382,5796,6210,6624,7038,

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 414, 419 which is 173466

So, the LCM of 414, 419 is 173466.

One method for determining the LCM of 414 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 414's prime factorization:

Prime factors of 414 are 2, 3,23.

414 = 2¹×3²×23¹

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: 2, 3,23,419

2¹×3²×23¹×419¹ = 173466

This shows that the LCM of 414 and 419 is 173466.

The first step in determining the Least Common Multiple of 414 and 419 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 414 and 419:

Lets look at the first ten multiples of these numbers, 414 and 419:

414,828,1242,1656,2070,2484,2898,3312,3726,7038 are the first ten multiples of 414.

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 414 and 419, for example, are 4968, 7038, and 6704. 173466 is the least common multiple since it is the smallest.

414 and 419 have an LCM of 173466.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 414 and 419, than apply into the LCM equation.

GCF(414,419) = 1
LCM(414,419) = ( 414 × 419) / 1
LCM(414,419) = 173466 / 1
LCM(414,419) = 173466

1. What is the LCM of 414 and 419?

The LCM of 414 and 419 is 173466.

2. How to find the lowest common multiple of 414 and 419?

To find the lowest common multiple of 414 and 419, we have to get the multip;es of both numbers and identify the least common multiple in them which is 173466.

3. What are the Factors of 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

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 414 and 419 = 173466

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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 = 173466 = 2 x 3 x 3 x 23 x 419

Step 4: Therefore, the least common multiple of 414 and 419 is 173466.