LCM of 38 and 45
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 38 and 45 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1710 as output. Here you can check the answer for Find the LCM of 38 and 45.
What is LCM of 38 and 45
Given Numbers are 38, 45
We can find the LCM of 38, 45 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 38 and 45
Multiples of 38 =38,76,114,152,190,228,266,304,342,380,418,456,494,532,570,608,646,
Multiples of 45 =45,90,135,180,225,270,315,360,405,450,495,540,585,630,675,720,765,
Now, get the least common multiple of 38, 45 which is 1710
So, the LCM of 38, 45 is 1710.
Least Common Multiple (LCM) of 38 and 45 with the help of Prime Factorisation
One method for determining the LCM of 38 and 45 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 38's prime factorization:
| 2 | 38 |
| 19 | 19 |
| 1 |
Prime factors of 38 are 2,19.
38 = 21×191
And this is 45's prime factorization:
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 45 are 3,5.
45 = 32×51
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: 2,19, 3,5
.21×32×51×191 = 1710
This shows that the LCM of 38 and 45 is 1710.
How to Calculate the LCM of 38 and 45 Using Common Multiples
The first step in determining the Least Common Multiple of 38 and 45 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 38 and 45:
Lets look at the first ten multiples of these numbers, 38 and 45:
38,76,114,152,190,228,266,304,342,646 are the first ten multiples of 38.
45,90,135,180,225,270,315,360,405,765 are the first ten multiples of 45.
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 38 and 45, for example, are 456, 646, and 720. 1710 is the least common multiple since it is the smallest.
38 and 45 have an LCM of 1710.
Least Common Multiple of 38 and 45 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 45, than apply into the LCM equation.
GCF(38,45) = 1
LCM(38,45) = ( 38 × 45) / 1
LCM(38,45) = 1710 / 1
LCM(38,45) = 1710
Related Least Common Multiples of 38
Related Least Common Multiples of 45
Frequently Asked Questions on LCM of 38 and 45
1. What is the LCM of 38 and 45?
The LCM of 38 and 45 is 1710.
2. How to find the lowest common multiple of 38 and 45?
To find the lowest common multiple of 38 and 45, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1710.
3. 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.
4. What are the Factors of 45?
Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.
5. How to Find the LCM of 38 and 45?Answer:
Least Common Multiple of 38 and 45 = 1710
Step 1: Find the prime factorization of 38
38 = 2 x 19
Step 2: Find the prime factorization of 45
45 = 3 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 = 1710 = 2 x 3 x 3 x 5 x 19
Step 4: Therefore, the least common multiple of 38 and 45 is 1710.