LCM of 36 and 45
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 36 and 45 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 180 as output. Here you can check the answer for Find the LCM of 36 and 45.
What is LCM of 36 and 45
Given Numbers are 36, 45
We can find the LCM of 36, 45 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 36 and 45
Multiples of 36 =36,72,108,144,180,216,252,288,324,360,396,432,468,504,540,576,612,
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 36, 45 which is 180
So, the LCM of 36, 45 is 180.
Least Common Multiple (LCM) of 36 and 45 with the help of Prime Factorisation
One method for determining the LCM of 36 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 36's prime factorization:
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 36 are 2,3.
36 = 22×32
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: 2,3,5
.22×32×51 = 180
This shows that the LCM of 36 and 45 is 180.
How to Calculate the LCM of 36 and 45 Using Common Multiples
The first step in determining the Least Common Multiple of 36 and 45 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 36 and 45:
Lets look at the first ten multiples of these numbers, 36 and 45:
36,72,108,144,180,216,252,288,324,612 are the first ten multiples of 36.
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 36 and 45, for example, are 432, 612, and 720. 180 is the least common multiple since it is the smallest.
36 and 45 have an LCM of 180.
Least Common Multiple of 36 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 36 and 45, than apply into the LCM equation.
GCF(36,45) = 9
LCM(36,45) = ( 36 × 45) / 9
LCM(36,45) = 1620 / 9
LCM(36,45) = 180
Related Least Common Multiples of 36
Related Least Common Multiples of 45
Frequently Asked Questions on LCM of 36 and 45
1. What is the LCM of 36 and 45?
The LCM of 36 and 45 is 180.
2. How to find the lowest common multiple of 36 and 45?
To find the lowest common multiple of 36 and 45, we have to get the multip;es of both numbers and identify the least common multiple in them which is 180.
3. What are the Factors of 36?
Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.
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 36 and 45?Answer:
Least Common Multiple of 36 and 45 = 180
Step 1: Find the prime factorization of 36
36 = 2 x 2 x 3 x 3
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 = 180 = 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 36 and 45 is 180.