Given Numbers are 408, 416

We can find the LCM of 408, 416 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 408 and 416

Multiples of 408 =408,816,1224,1632,2040,2448,2856,3264,3672,4080,4488,4896,5304,5712,6120,6528,6936,

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 408, 416 which is 21216

So, the LCM of 408, 416 is 21216.

One method for determining the LCM of 408 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 408's prime factorization:

Prime factors of 408 are 2, 3,17.

408 = 2³×3¹×17¹

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, 3,17,13

2⁵×3¹×13¹×17¹ = 21216

This shows that the LCM of 408 and 416 is 21216.

The first step in determining the Least Common Multiple of 408 and 416 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 408 and 416:

Lets look at the first ten multiples of these numbers, 408 and 416:

408,816,1224,1632,2040,2448,2856,3264,3672,6936 are the first ten multiples of 408.

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 408 and 416, for example, are 4896, 6936, and 6656. 21216 is the least common multiple since it is the smallest.

408 and 416 have an LCM of 21216.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 408 and 416, than apply into the LCM equation.

GCF(408,416) = 8
LCM(408,416) = ( 408 × 416) / 8
LCM(408,416) = 169728 / 8
LCM(408,416) = 21216

1. What is the LCM of 408 and 416?

The LCM of 408 and 416 is 21216.

2. How to find the lowest common multiple of 408 and 416?

To find the lowest common multiple of 408 and 416, we have to get the multip;es of both numbers and identify the least common multiple in them which is 21216.

3. What are the Factors of 408?

Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.

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 408 and 416 = 21216

Step 1: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

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 = 21216 = 2 x 2 x 2 x 2 x 2 x 3 x 13 x 17

Step 4: Therefore, the least common multiple of 408 and 416 is 21216.