Given Numbers are 17, 21

We can find the LCM of 17, 21 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 17 and 21

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

Multiples of 21 =21,42,63,84,105,126,147,168,189,210,231,252,273,294,315,336,357,

Now, get the least common multiple of 17, 21 which is 357

So, the LCM of 17, 21 is 357.

One method for determining the LCM of 17 and 21 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 21's prime factorization:

Prime factors of 21 are 3,7.

21 = 3¹×7¹

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, 3,7

3¹×7¹×17¹ = 357

This shows that the LCM of 17 and 21 is 357.

The first step in determining the Least Common Multiple of 17 and 21 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 17 and 21:

Lets look at the first ten multiples of these numbers, 17 and 21:

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

21,42,63,84,105,126,147,168,189,357 are the first ten multiples of 21.

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 21, for example, are 204, 289, and 336. 357 is the least common multiple since it is the smallest.

17 and 21 have an LCM of 357.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 21, than apply into the LCM equation.

GCF(17,21) = 1
LCM(17,21) = ( 17 × 21) / 1
LCM(17,21) = 357 / 1
LCM(17,21) = 357

1. What is the LCM of 17 and 21?

The LCM of 17 and 21 is 357.

2. How to find the lowest common multiple of 17 and 21?

To find the lowest common multiple of 17 and 21, we have to get the multip;es of both numbers and identify the least common multiple in them which is 357.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

Answer:

Least Common Multiple of 17 and 21 = 357

Step 1: Find the prime factorization of 17

17 = 17

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

LCM = 357 = 3 x 7 x 17

Step 4: Therefore, the least common multiple of 17 and 21 is 357.