Given Numbers are 17, 25

We can find the LCM of 17, 25 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 17 and 25

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

Multiples of 25 =25,50,75,100,125,150,175,200,225,250,275,300,325,350,375,400,425,

Now, get the least common multiple of 17, 25 which is 425

So, the LCM of 17, 25 is 425.

One method for determining the LCM of 17 and 25 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 25's prime factorization:

Prime factors of 25 are 5.

25 = 5²

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:17,5

5²×17¹ = 425

This shows that the LCM of 17 and 25 is 425.

The first step in determining the Least Common Multiple of 17 and 25 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 17 and 25:

Lets look at the first ten multiples of these numbers, 17 and 25:

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

25,50,75,100,125,150,175,200,225,425 are the first ten multiples of 25.

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 25, for example, are 204, 289, and 400. 425 is the least common multiple since it is the smallest.

17 and 25 have an LCM of 425.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 25, than apply into the LCM equation.

GCF(17,25) = 1
LCM(17,25) = ( 17 × 25) / 1
LCM(17,25) = 425 / 1
LCM(17,25) = 425

1. What is the LCM of 17 and 25?

The LCM of 17 and 25 is 425.

2. How to find the lowest common multiple of 17 and 25?

To find the lowest common multiple of 17 and 25, we have to get the multip;es of both numbers and identify the least common multiple in them which is 425.

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 25?

Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.

Answer:

Least Common Multiple of 17 and 25 = 425

Step 1: Find the prime factorization of 17

17 = 17

Step 2: Find the prime factorization of 25

25 = 5 x 5

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

LCM = 425 = 5 x 5 x 17

Step 4: Therefore, the least common multiple of 17 and 25 is 425.