LCM of 39 and 45
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 39 and 45 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 585 as output. Here you can check the answer for Find the LCM of 39 and 45.
What is LCM of 39 and 45
Given Numbers are 39, 45
We can find the LCM of 39, 45 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 39 and 45
Multiples of 39 =39,78,117,156,195,234,273,312,351,390,429,468,507,546,585,624,663,
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 39, 45 which is 585
So, the LCM of 39, 45 is 585.
Least Common Multiple (LCM) of 39 and 45 with the help of Prime Factorisation
One method for determining the LCM of 39 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 39's prime factorization:
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 39 are 3,13.
39 = 31×131
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: 3,13,5
.32×51×131 = 585
This shows that the LCM of 39 and 45 is 585.
How to Calculate the LCM of 39 and 45 Using Common Multiples
The first step in determining the Least Common Multiple of 39 and 45 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 39 and 45:
Lets look at the first ten multiples of these numbers, 39 and 45:
39,78,117,156,195,234,273,312,351,663 are the first ten multiples of 39.
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 39 and 45, for example, are 468, 663, and 720. 585 is the least common multiple since it is the smallest.
39 and 45 have an LCM of 585.
Least Common Multiple of 39 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 39 and 45, than apply into the LCM equation.
GCF(39,45) = 3
LCM(39,45) = ( 39 × 45) / 3
LCM(39,45) = 1755 / 3
LCM(39,45) = 585
Related Least Common Multiples of 39
Related Least Common Multiples of 45
Frequently Asked Questions on LCM of 39 and 45
1. What is the LCM of 39 and 45?
The LCM of 39 and 45 is 585.
2. How to find the lowest common multiple of 39 and 45?
To find the lowest common multiple of 39 and 45, we have to get the multip;es of both numbers and identify the least common multiple in them which is 585.
3. What are the Factors of 39?
Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.
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 39 and 45?Answer:
Least Common Multiple of 39 and 45 = 585
Step 1: Find the prime factorization of 39
39 = 3 x 13
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 = 585 = 3 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 39 and 45 is 585.