LCM of 17 and 24
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 17 and 24 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 408 as output. Here you can check the answer for Find the LCM of 17 and 24.
What is LCM of 17 and 24
Given Numbers are 17, 24
We can find the LCM of 17, 24 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 17 and 24
Multiples of 17 =17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272,289,
Multiples of 24 =24,48,72,96,120,144,168,192,216,240,264,288,312,336,360,384,408,
Now, get the least common multiple of 17, 24 which is 408
So, the LCM of 17, 24 is 408.
Least Common Multiple (LCM) of 17 and 24 with the help of Prime Factorisation
One method for determining the LCM of 17 and 24 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:
| 17 | 17 |
| 1 |
Prime factors of 17 are 17.
17 = 171
And this is 24's prime factorization:
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 24 are 2,3.
24 = 23×31
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, 2,3
.23×31×171 = 408
This shows that the LCM of 17 and 24 is 408.
How to Calculate the LCM of 17 and 24 Using Common Multiples
The first step in determining the Least Common Multiple of 17 and 24 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 17 and 24:
Lets look at the first ten multiples of these numbers, 17 and 24:
17,34,51,68,85,102,119,136,153,289 are the first ten multiples of 17.
24,48,72,96,120,144,168,192,216,408 are the first ten multiples of 24.
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 24, for example, are 204, 289, and 384. 408 is the least common multiple since it is the smallest.
17 and 24 have an LCM of 408.
Least Common Multiple of 17 and 24 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 24, than apply into the LCM equation.
GCF(17,24) = 1
LCM(17,24) = ( 17 × 24) / 1
LCM(17,24) = 408 / 1
LCM(17,24) = 408
Related Least Common Multiples of 17
Related Least Common Multiples of 24
Frequently Asked Questions on LCM of 17 and 24
1. What is the LCM of 17 and 24?
The LCM of 17 and 24 is 408.
2. How to find the lowest common multiple of 17 and 24?
To find the lowest common multiple of 17 and 24, we have to get the multip;es of both numbers and identify the least common multiple in them which is 408.
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 24?
Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.
5. How to Find the LCM of 17 and 24?Answer:
Least Common Multiple of 17 and 24 = 408
Step 1: Find the prime factorization of 17
17 = 17
Step 2: Find the prime factorization of 24
24 = 2 x 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 408 = 2 x 2 x 2 x 3 x 17
Step 4: Therefore, the least common multiple of 17 and 24 is 408.