Given Numbers are 403, 408

We can find the LCM of 403, 408 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 403 and 408

Multiples of 403 =403,806,1209,1612,2015,2418,2821,3224,3627,4030,4433,4836,5239,5642,6045,6448,6851,

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 403, 408 which is 164424

So, the LCM of 403, 408 is 164424.

One method for determining the LCM of 403 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 403's prime factorization:

Prime factors of 403 are 13,31.

403 = 13¹×31¹

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: 13,31, 2, 3,17

2³×3¹×13¹×17¹×31¹ = 164424

This shows that the LCM of 403 and 408 is 164424.

The first step in determining the Least Common Multiple of 403 and 408 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 403 and 408:

Lets look at the first ten multiples of these numbers, 403 and 408:

403,806,1209,1612,2015,2418,2821,3224,3627,6851 are the first ten multiples of 403.

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 403 and 408, for example, are 4836, 6851, and 6528. 164424 is the least common multiple since it is the smallest.

403 and 408 have an LCM of 164424.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 403 and 408, than apply into the LCM equation.

GCF(403,408) = 1
LCM(403,408) = ( 403 × 408) / 1
LCM(403,408) = 164424 / 1
LCM(403,408) = 164424

1. What is the LCM of 403 and 408?

The LCM of 403 and 408 is 164424.

2. How to find the lowest common multiple of 403 and 408?

To find the lowest common multiple of 403 and 408, we have to get the multip;es of both numbers and identify the least common multiple in them which is 164424.

3. What are the Factors of 403?

Answer: Factors of 403 are 1, 13, 31, 403. There are 4 integers that are factors of 403. The greatest factor of 403 is 403.

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 403 and 408 = 164424

Step 1: Find the prime factorization of 403

403 = 13 x 31

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 = 164424 = 2 x 2 x 2 x 3 x 13 x 17 x 31

Step 4: Therefore, the least common multiple of 403 and 408 is 164424.