LCM of 15 and 23
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 15 and 23 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 345 as output. Here you can check the answer for Find the LCM of 15 and 23.
What is LCM of 15 and 23
Given Numbers are 15, 23
We can find the LCM of 15, 23 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 15 and 23
Multiples of 15 =15,30,45,60,75,90,105,120,135,150,165,180,195,210,225,240,255,
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 15, 23 which is 345
So, the LCM of 15, 23 is 345.
Least Common Multiple (LCM) of 15 and 23 with the help of Prime Factorisation
One method for determining the LCM of 15 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 15's prime factorization:
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 15 are 3,5.
15 = 31×51
And this is 23's prime factorization:
| 23 | 23 |
| 1 |
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: 3,5,23
.31×51×231 = 345
This shows that the LCM of 15 and 23 is 345.
How to Calculate the LCM of 15 and 23 Using Common Multiples
The first step in determining the Least Common Multiple of 15 and 23 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 15 and 23:
Lets look at the first ten multiples of these numbers, 15 and 23:
15,30,45,60,75,90,105,120,135,255 are the first ten multiples of 15.
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 15 and 23, for example, are 180, 255, and 368. 345 is the least common multiple since it is the smallest.
15 and 23 have an LCM of 345.
Least Common Multiple of 15 and 23 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 23, than apply into the LCM equation.
GCF(15,23) = 1
LCM(15,23) = ( 15 × 23) / 1
LCM(15,23) = 345 / 1
LCM(15,23) = 345
Related Least Common Multiples of 15
Related Least Common Multiples of 23
Frequently Asked Questions on LCM of 15 and 23
1. What is the LCM of 15 and 23?
The LCM of 15 and 23 is 345.
2. How to find the lowest common multiple of 15 and 23?
To find the lowest common multiple of 15 and 23, we have to get the multip;es of both numbers and identify the least common multiple in them which is 345.
3. What are the Factors of 15?
Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.
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.
5. How to Find the LCM of 15 and 23?Answer:
Least Common Multiple of 15 and 23 = 345
Step 1: Find the prime factorization of 15
15 = 3 x 5
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 = 345 = 3 x 5 x 23
Step 4: Therefore, the least common multiple of 15 and 23 is 345.