Given Numbers are 17, 23

We can find the LCM of 17, 23 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 17 and 23

Multiples of 17 =17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272,289,

Multiples of 23 =23,46,69,92,115,138,161,184,207,230,253,276,299,322,345,368,391,

Now, get the least common multiple of 17, 23 which is 391

So, the LCM of 17, 23 is 391.

One method for determining the LCM of 17 and 23 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 17's prime factorization:

Prime factors of 17 are 17.

17 = 17¹

And this is 23's prime factorization:

Prime factors of 23 are 23.

23 = 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:17,23

17¹×23¹ = 391

This shows that the LCM of 17 and 23 is 391.

The first step in determining the Least Common Multiple of 17 and 23 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 17 and 23:

Lets look at the first ten multiples of these numbers, 17 and 23:

17,34,51,68,85,102,119,136,153,289 are the first ten multiples of 17.

23,46,69,92,115,138,161,184,207,391 are the first ten multiples of 23.

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 17 and 23, for example, are 204, 289, and 368. 391 is the least common multiple since it is the smallest.

17 and 23 have an LCM of 391.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 23, than apply into the LCM equation.

GCF(17,23) = 1
LCM(17,23) = ( 17 × 23) / 1
LCM(17,23) = 391 / 1
LCM(17,23) = 391

1. What is the LCM of 17 and 23?

The LCM of 17 and 23 is 391.

2. How to find the lowest common multiple of 17 and 23?

To find the lowest common multiple of 17 and 23, we have to get the multip;es of both numbers and identify the least common multiple in them which is 391.

3. What are the Factors of 17?

Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.

4. What are the Factors of 23?

Answer: Factors of 23 are 1, 23. There are 2 integers that are factors of 23. The greatest factor of 23 is 23.

Answer:

Least Common Multiple of 17 and 23 = 391

Step 1: Find the prime factorization of 17

17 = 17

Step 2: Find the prime factorization of 23

23 = 23

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

LCM = 391 = 17 x 23

Step 4: Therefore, the least common multiple of 17 and 23 is 391.