Given Numbers are 407, 414

We can find the LCM of 407, 414 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 407 and 414

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

Multiples of 414 =414,828,1242,1656,2070,2484,2898,3312,3726,4140,4554,4968,5382,5796,6210,6624,7038,

Now, get the least common multiple of 407, 414 which is 168498

So, the LCM of 407, 414 is 168498.

One method for determining the LCM of 407 and 414 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 407's prime factorization:

Prime factors of 407 are 11,37.

407 = 11¹×37¹

And this is 414's prime factorization:

Prime factors of 414 are 2, 3,23.

414 = 2¹×3²×23¹

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: 11,37, 2, 3,23

2¹×3²×11¹×23¹×37¹ = 168498

This shows that the LCM of 407 and 414 is 168498.

The first step in determining the Least Common Multiple of 407 and 414 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 407 and 414:

Lets look at the first ten multiples of these numbers, 407 and 414:

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

414,828,1242,1656,2070,2484,2898,3312,3726,7038 are the first ten multiples of 414.

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 407 and 414, for example, are 4884, 6919, and 6624. 168498 is the least common multiple since it is the smallest.

407 and 414 have an LCM of 168498.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 407 and 414, than apply into the LCM equation.

GCF(407,414) = 1
LCM(407,414) = ( 407 × 414) / 1
LCM(407,414) = 168498 / 1
LCM(407,414) = 168498

1. What is the LCM of 407 and 414?

The LCM of 407 and 414 is 168498.

2. How to find the lowest common multiple of 407 and 414?

To find the lowest common multiple of 407 and 414, we have to get the multip;es of both numbers and identify the least common multiple in them which is 168498.

3. 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.

4. What are the Factors of 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

Answer:

Least Common Multiple of 407 and 414 = 168498

Step 1: Find the prime factorization of 407

407 = 11 x 37

Step 2: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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

LCM = 168498 = 2 x 3 x 3 x 11 x 23 x 37

Step 4: Therefore, the least common multiple of 407 and 414 is 168498.