LCM of 23 and 30
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 23 and 30 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 690 as output. Here you can check the answer for Find the LCM of 23 and 30.
What is LCM of 23 and 30
Given Numbers are 23, 30
We can find the LCM of 23, 30 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 23 and 30
Multiples of 23 =23,46,69,92,115,138,161,184,207,230,253,276,299,322,345,368,391,
Multiples of 30 =30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,
Now, get the least common multiple of 23, 30 which is 690
So, the LCM of 23, 30 is 690.
Least Common Multiple (LCM) of 23 and 30 with the help of Prime Factorisation
One method for determining the LCM of 23 and 30 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 23's prime factorization:
| 23 | 23 |
| 1 |
Prime factors of 23 are 23.
23 = 231
And this is 30's prime factorization:
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 30 are 2, 3,5.
30 = 21×31×51
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:23, 2, 3,5
.21×31×51×231 = 690
This shows that the LCM of 23 and 30 is 690.
How to Calculate the LCM of 23 and 30 Using Common Multiples
The first step in determining the Least Common Multiple of 23 and 30 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 23 and 30:
Lets look at the first ten multiples of these numbers, 23 and 30:
23,46,69,92,115,138,161,184,207,391 are the first ten multiples of 23.
30,60,90,120,150,180,210,240,270,510 are the first ten multiples of 30.
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 23 and 30, for example, are 276, 391, and 480. 690 is the least common multiple since it is the smallest.
23 and 30 have an LCM of 690.
Least Common Multiple of 23 and 30 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23 and 30, than apply into the LCM equation.
GCF(23,30) = 1
LCM(23,30) = ( 23 × 30) / 1
LCM(23,30) = 690 / 1
LCM(23,30) = 690
Related Least Common Multiples of 23
Related Least Common Multiples of 30
Frequently Asked Questions on LCM of 23 and 30
1. What is the LCM of 23 and 30?
The LCM of 23 and 30 is 690.
2. How to find the lowest common multiple of 23 and 30?
To find the lowest common multiple of 23 and 30, we have to get the multip;es of both numbers and identify the least common multiple in them which is 690.
3. 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.
4. What are the Factors of 30?
Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.
5. How to Find the LCM of 23 and 30?Answer:
Least Common Multiple of 23 and 30 = 690
Step 1: Find the prime factorization of 23
23 = 23
Step 2: Find the prime factorization of 30
30 = 2 x 3 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 = 690 = 2 x 3 x 5 x 23
Step 4: Therefore, the least common multiple of 23 and 30 is 690.