Given Numbers are 414, 418

We can find the LCM of 414, 418 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 414 and 418

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

Multiples of 418 =418,836,1254,1672,2090,2508,2926,3344,3762,4180,4598,5016,5434,5852,6270,6688,7106,

Now, get the least common multiple of 414, 418 which is 86526

So, the LCM of 414, 418 is 86526.

One method for determining the LCM of 414 and 418 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 418's prime factorization:

Prime factors of 418 are 2, 11,19.

418 = 2¹×11¹×19¹

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, 11,19

2¹×3²×11¹×19¹×23¹ = 86526

This shows that the LCM of 414 and 418 is 86526.

The first step in determining the Least Common Multiple of 414 and 418 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 414 and 418:

Lets look at the first ten multiples of these numbers, 414 and 418:

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

418,836,1254,1672,2090,2508,2926,3344,3762,7106 are the first ten multiples of 418.

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 418, for example, are 4968, 7038, and 6688. 86526 is the least common multiple since it is the smallest.

414 and 418 have an LCM of 86526.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 414 and 418, than apply into the LCM equation.

GCF(414,418) = 2
LCM(414,418) = ( 414 × 418) / 2
LCM(414,418) = 173052 / 2
LCM(414,418) = 86526

1. What is the LCM of 414 and 418?

The LCM of 414 and 418 is 86526.

2. How to find the lowest common multiple of 414 and 418?

To find the lowest common multiple of 414 and 418, we have to get the multip;es of both numbers and identify the least common multiple in them which is 86526.

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 418?

Answer: Factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418. There are 8 integers that are factors of 418. The greatest factor of 418 is 418.

Answer:

Least Common Multiple of 414 and 418 = 86526

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

Step 2: Find the prime factorization of 418

418 = 2 x 11 x 19

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

LCM = 86526 = 2 x 3 x 3 x 11 x 19 x 23

Step 4: Therefore, the least common multiple of 414 and 418 is 86526.