Given Numbers are 403, 409

We can find the LCM of 403, 409 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 403 and 409

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

Multiples of 409 =409,818,1227,1636,2045,2454,2863,3272,3681,4090,4499,4908,5317,5726,6135,6544,6953,

Now, get the least common multiple of 403, 409 which is 164827

So, the LCM of 403, 409 is 164827.

One method for determining the LCM of 403 and 409 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 409's prime factorization:

Prime factors of 409 are 409.

409 = 409¹

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: 13,31,409

13¹×31¹×409¹ = 164827

This shows that the LCM of 403 and 409 is 164827.

The first step in determining the Least Common Multiple of 403 and 409 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 403 and 409:

Lets look at the first ten multiples of these numbers, 403 and 409:

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

409,818,1227,1636,2045,2454,2863,3272,3681,6953 are the first ten multiples of 409.

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 409, for example, are 4836, 6851, and 6544. 164827 is the least common multiple since it is the smallest.

403 and 409 have an LCM of 164827.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 403 and 409, than apply into the LCM equation.

GCF(403,409) = 1
LCM(403,409) = ( 403 × 409) / 1
LCM(403,409) = 164827 / 1
LCM(403,409) = 164827

1. What is the LCM of 403 and 409?

The LCM of 403 and 409 is 164827.

2. How to find the lowest common multiple of 403 and 409?

To find the lowest common multiple of 403 and 409, we have to get the multip;es of both numbers and identify the least common multiple in them which is 164827.

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 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

Answer:

Least Common Multiple of 403 and 409 = 164827

Step 1: Find the prime factorization of 403

403 = 13 x 31

Step 2: Find the prime factorization of 409

409 = 409

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

LCM = 164827 = 13 x 31 x 409

Step 4: Therefore, the least common multiple of 403 and 409 is 164827.