Given Numbers are 412, 416

We can find the LCM of 412, 416 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 412 and 416

Multiples of 412 =412,824,1236,1648,2060,2472,2884,3296,3708,4120,4532,4944,5356,5768,6180,6592,7004,

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

Now, get the least common multiple of 412, 416 which is 42848

So, the LCM of 412, 416 is 42848.

One method for determining the LCM of 412 and 416 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 412's prime factorization:

Prime factors of 412 are 2,103.

412 = 2²×103¹

And this is 416's prime factorization:

Prime factors of 416 are 2,13.

416 = 2⁵×13¹

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: 2,103,13

2⁵×13¹×103¹ = 42848

This shows that the LCM of 412 and 416 is 42848.

The first step in determining the Least Common Multiple of 412 and 416 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 412 and 416:

Lets look at the first ten multiples of these numbers, 412 and 416:

412,824,1236,1648,2060,2472,2884,3296,3708,7004 are the first ten multiples of 412.

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

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 412 and 416, for example, are 4944, 7004, and 6656. 42848 is the least common multiple since it is the smallest.

412 and 416 have an LCM of 42848.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 412 and 416, than apply into the LCM equation.

GCF(412,416) = 4
LCM(412,416) = ( 412 × 416) / 4
LCM(412,416) = 171392 / 4
LCM(412,416) = 42848

1. What is the LCM of 412 and 416?

The LCM of 412 and 416 is 42848.

2. How to find the lowest common multiple of 412 and 416?

To find the lowest common multiple of 412 and 416, we have to get the multip;es of both numbers and identify the least common multiple in them which is 42848.

3. What are the Factors of 412?

Answer: Factors of 412 are 1, 2, 4, 103, 206, 412. There are 6 integers that are factors of 412. The greatest factor of 412 is 412.

4. 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.

Answer:

Least Common Multiple of 412 and 416 = 42848

Step 1: Find the prime factorization of 412

412 = 2 x 2 x 103

Step 2: Find the prime factorization of 416

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

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

LCM = 42848 = 2 x 2 x 2 x 2 x 2 x 13 x 103

Step 4: Therefore, the least common multiple of 412 and 416 is 42848.