Given Numbers are 416, 422

We can find the LCM of 416, 422 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 416 and 422

Multiples of 416 =416,832,1248,1664,2080,2496,2912,3328,3744,4160,4576,4992,5408,5824,6240,6656,7072,

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 416, 422 which is 87776

So, the LCM of 416, 422 is 87776.

One method for determining the LCM of 416 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 416's prime factorization:

Prime factors of 416 are 2,13.

416 = 2⁵×13¹

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: 2,13,211

2⁵×13¹×211¹ = 87776

This shows that the LCM of 416 and 422 is 87776.

The first step in determining the Least Common Multiple of 416 and 422 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 416 and 422:

Lets look at the first ten multiples of these numbers, 416 and 422:

416,832,1248,1664,2080,2496,2912,3328,3744,7072 are the first ten multiples of 416.

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 416 and 422, for example, are 4992, 7072, and 6752. 87776 is the least common multiple since it is the smallest.

416 and 422 have an LCM of 87776.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 416 and 422, than apply into the LCM equation.

GCF(416,422) = 2
LCM(416,422) = ( 416 × 422) / 2
LCM(416,422) = 175552 / 2
LCM(416,422) = 87776

1. What is the LCM of 416 and 422?

The LCM of 416 and 422 is 87776.

2. How to find the lowest common multiple of 416 and 422?

To find the lowest common multiple of 416 and 422, we have to get the multip;es of both numbers and identify the least common multiple in them which is 87776.

3. What are the Factors of 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

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 416 and 422 = 87776

Step 1: Find the prime factorization of 416

416 = 2 x 2 x 2 x 2 x 2 x 13

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 = 87776 = 2 x 2 x 2 x 2 x 2 x 13 x 211

Step 4: Therefore, the least common multiple of 416 and 422 is 87776.