LCM of 30 and 34
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 30 and 34 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 510 as output. Here you can check the answer for Find the LCM of 30 and 34.
What is LCM of 30 and 34
Given Numbers are 30, 34
We can find the LCM of 30, 34 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 30 and 34
Multiples of 30 =30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,
Multiples of 34 =34,68,102,136,170,204,238,272,306,340,374,408,442,476,510,544,578,
Now, get the least common multiple of 30, 34 which is 510
So, the LCM of 30, 34 is 510.
Least Common Multiple (LCM) of 30 and 34 with the help of Prime Factorisation
One method for determining the LCM of 30 and 34 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 30's prime factorization:
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 30 are 2, 3,5.
30 = 21×31×51
And this is 34's prime factorization:
| 2 | 34 |
| 17 | 17 |
| 1 |
Prime factors of 34 are 2,17.
34 = 21×171
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: 2, 3,5,17
.21×31×51×171 = 510
This shows that the LCM of 30 and 34 is 510.
How to Calculate the LCM of 30 and 34 Using Common Multiples
The first step in determining the Least Common Multiple of 30 and 34 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 30 and 34:
Lets look at the first ten multiples of these numbers, 30 and 34:
30,60,90,120,150,180,210,240,270,510 are the first ten multiples of 30.
34,68,102,136,170,204,238,272,306,578 are the first ten multiples of 34.
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 30 and 34, for example, are 360, 510, and 544. 510 is the least common multiple since it is the smallest.
30 and 34 have an LCM of 510.
Least Common Multiple of 30 and 34 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 34, than apply into the LCM equation.
GCF(30,34) = 2
LCM(30,34) = ( 30 × 34) / 2
LCM(30,34) = 1020 / 2
LCM(30,34) = 510
Related Least Common Multiples of 30
Related Least Common Multiples of 34
Frequently Asked Questions on LCM of 30 and 34
1. What is the LCM of 30 and 34?
The LCM of 30 and 34 is 510.
2. How to find the lowest common multiple of 30 and 34?
To find the lowest common multiple of 30 and 34, we have to get the multip;es of both numbers and identify the least common multiple in them which is 510.
3. 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.
4. What are the Factors of 34?
Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.
5. How to Find the LCM of 30 and 34?Answer:
Least Common Multiple of 30 and 34 = 510
Step 1: Find the prime factorization of 30
30 = 2 x 3 x 5
Step 2: Find the prime factorization of 34
34 = 2 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 510 = 2 x 3 x 5 x 17
Step 4: Therefore, the least common multiple of 30 and 34 is 510.