Given Numbers are 414, 422

We can find the LCM of 414, 422 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 414 and 422

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

Multiples of 422 =422,844,1266,1688,2110,2532,2954,3376,3798,4220,4642,5064,5486,5908,6330,6752,7174,

Now, get the least common multiple of 414, 422 which is 87354

So, the LCM of 414, 422 is 87354.

One method for determining the LCM of 414 and 422 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 422's prime factorization:

Prime factors of 422 are 2,211.

422 = 2¹×211¹

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, 3,23,211

2¹×3²×23¹×211¹ = 87354

This shows that the LCM of 414 and 422 is 87354.

The first step in determining the Least Common Multiple of 414 and 422 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 414 and 422:

Lets look at the first ten multiples of these numbers, 414 and 422:

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

422,844,1266,1688,2110,2532,2954,3376,3798,7174 are the first ten multiples of 422.

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 422, for example, are 4968, 7038, and 6752. 87354 is the least common multiple since it is the smallest.

414 and 422 have an LCM of 87354.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 414 and 422, than apply into the LCM equation.

GCF(414,422) = 2
LCM(414,422) = ( 414 × 422) / 2
LCM(414,422) = 174708 / 2
LCM(414,422) = 87354

1. What is the LCM of 414 and 422?

The LCM of 414 and 422 is 87354.

2. How to find the lowest common multiple of 414 and 422?

To find the lowest common multiple of 414 and 422, we have to get the multip;es of both numbers and identify the least common multiple in them which is 87354.

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 422?

Answer: Factors of 422 are 1, 2, 211, 422. There are 4 integers that are factors of 422. The greatest factor of 422 is 422.

Answer:

Least Common Multiple of 414 and 422 = 87354

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

Step 2: Find the prime factorization of 422

422 = 2 x 211

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

LCM = 87354 = 2 x 3 x 3 x 23 x 211

Step 4: Therefore, the least common multiple of 414 and 422 is 87354.