LCM of 30 and 38
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 30 and 38 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 570 as output. Here you can check the answer for Find the LCM of 30 and 38.
What is LCM of 30 and 38
Given Numbers are 30, 38
We can find the LCM of 30, 38 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 30 and 38
Multiples of 30 =30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,
Multiples of 38 =38,76,114,152,190,228,266,304,342,380,418,456,494,532,570,608,646,
Now, get the least common multiple of 30, 38 which is 570
So, the LCM of 30, 38 is 570.
Least Common Multiple (LCM) of 30 and 38 with the help of Prime Factorisation
One method for determining the LCM of 30 and 38 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 38's prime factorization:
| 2 | 38 |
| 19 | 19 |
| 1 |
Prime factors of 38 are 2,19.
38 = 21×191
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, 3,5,19
.21×31×51×191 = 570
This shows that the LCM of 30 and 38 is 570.
How to Calculate the LCM of 30 and 38 Using Common Multiples
The first step in determining the Least Common Multiple of 30 and 38 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 30 and 38:
Lets look at the first ten multiples of these numbers, 30 and 38:
30,60,90,120,150,180,210,240,270,510 are the first ten multiples of 30.
38,76,114,152,190,228,266,304,342,646 are the first ten multiples of 38.
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 38, for example, are 360, 510, and 608. 570 is the least common multiple since it is the smallest.
30 and 38 have an LCM of 570.
Least Common Multiple of 30 and 38 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 38, than apply into the LCM equation.
GCF(30,38) = 2
LCM(30,38) = ( 30 × 38) / 2
LCM(30,38) = 1140 / 2
LCM(30,38) = 570
Related Least Common Multiples of 30
Related Least Common Multiples of 38
Frequently Asked Questions on LCM of 30 and 38
1. What is the LCM of 30 and 38?
The LCM of 30 and 38 is 570.
2. How to find the lowest common multiple of 30 and 38?
To find the lowest common multiple of 30 and 38, we have to get the multip;es of both numbers and identify the least common multiple in them which is 570.
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 38?
Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.
5. How to Find the LCM of 30 and 38?Answer:
Least Common Multiple of 30 and 38 = 570
Step 1: Find the prime factorization of 30
30 = 2 x 3 x 5
Step 2: Find the prime factorization of 38
38 = 2 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 570 = 2 x 3 x 5 x 19
Step 4: Therefore, the least common multiple of 30 and 38 is 570.