Given Numbers are 400, 407

We can find the LCM of 400, 407 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 400 and 407

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

Multiples of 407 =407,814,1221,1628,2035,2442,2849,3256,3663,4070,4477,4884,5291,5698,6105,6512,6919,

Now, get the least common multiple of 400, 407 which is 162800

So, the LCM of 400, 407 is 162800.

One method for determining the LCM of 400 and 407 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 407's prime factorization:

Prime factors of 407 are 11,37.

407 = 11¹×37¹

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, 11,37

2⁴×5²×11¹×37¹ = 162800

This shows that the LCM of 400 and 407 is 162800.

The first step in determining the Least Common Multiple of 400 and 407 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 400 and 407:

Lets look at the first ten multiples of these numbers, 400 and 407:

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

407,814,1221,1628,2035,2442,2849,3256,3663,6919 are the first ten multiples of 407.

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 407, for example, are 4800, 6800, and 6512. 162800 is the least common multiple since it is the smallest.

400 and 407 have an LCM of 162800.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 400 and 407, than apply into the LCM equation.

GCF(400,407) = 1
LCM(400,407) = ( 400 × 407) / 1
LCM(400,407) = 162800 / 1
LCM(400,407) = 162800

1. What is the LCM of 400 and 407?

The LCM of 400 and 407 is 162800.

2. How to find the lowest common multiple of 400 and 407?

To find the lowest common multiple of 400 and 407, we have to get the multip;es of both numbers and identify the least common multiple in them which is 162800.

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 407?

Answer: Factors of 407 are 1, 11, 37, 407. There are 4 integers that are factors of 407. The greatest factor of 407 is 407.

Answer:

Least Common Multiple of 400 and 407 = 162800

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 407

407 = 11 x 37

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

LCM = 162800 = 2 x 2 x 2 x 2 x 5 x 5 x 11 x 37

Step 4: Therefore, the least common multiple of 400 and 407 is 162800.