Given Numbers are 400, 408

We can find the LCM of 400, 408 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 400 and 408

Multiples of 400 =400,800,1200,1600,2000,2400,2800,3200,3600,4000,4400,4800,5200,5600,6000,6400,6800,

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

Now, get the least common multiple of 400, 408 which is 20400

So, the LCM of 400, 408 is 20400.

One method for determining the LCM of 400 and 408 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 400's prime factorization:

Prime factors of 400 are 2,5.

400 = 2⁴×5²

And this is 408's prime factorization:

Prime factors of 408 are 2, 3,17.

408 = 2³×3¹×17¹

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: 2,5, 3,17

2⁴×3¹×5²×17¹ = 20400

This shows that the LCM of 400 and 408 is 20400.

The first step in determining the Least Common Multiple of 400 and 408 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 400 and 408:

Lets look at the first ten multiples of these numbers, 400 and 408:

400,800,1200,1600,2000,2400,2800,3200,3600,6800 are the first ten multiples of 400.

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

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 400 and 408, for example, are 4800, 6800, and 6528. 20400 is the least common multiple since it is the smallest.

400 and 408 have an LCM of 20400.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 400 and 408, than apply into the LCM equation.

GCF(400,408) = 8
LCM(400,408) = ( 400 × 408) / 8
LCM(400,408) = 163200 / 8
LCM(400,408) = 20400

1. What is the LCM of 400 and 408?

The LCM of 400 and 408 is 20400.

2. How to find the lowest common multiple of 400 and 408?

To find the lowest common multiple of 400 and 408, we have to get the multip;es of both numbers and identify the least common multiple in them which is 20400.

3. What are the Factors of 400?

Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.

4. 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.

Answer:

Least Common Multiple of 400 and 408 = 20400

Step 1: Find the prime factorization of 400

400 = 2 x 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

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

LCM = 20400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 17

Step 4: Therefore, the least common multiple of 400 and 408 is 20400.