LCM of 40 and 45
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 40 and 45 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 360 as output. Here you can check the answer for Find the LCM of 40 and 45.
What is LCM of 40 and 45
Given Numbers are 40, 45
We can find the LCM of 40, 45 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 40 and 45
Multiples of 40 =40,80,120,160,200,240,280,320,360,400,440,480,520,560,600,640,680,
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 40, 45 which is 360
So, the LCM of 40, 45 is 360.
Least Common Multiple (LCM) of 40 and 45 with the help of Prime Factorisation
One method for determining the LCM of 40 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 40's prime factorization:
| 2 | 40 |
| 2 | 20 |
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 40 are 2,5.
40 = 23×51
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: 2,5,3
.23×32×51 = 360
This shows that the LCM of 40 and 45 is 360.
How to Calculate the LCM of 40 and 45 Using Common Multiples
The first step in determining the Least Common Multiple of 40 and 45 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 40 and 45:
Lets look at the first ten multiples of these numbers, 40 and 45:
40,80,120,160,200,240,280,320,360,680 are the first ten multiples of 40.
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 40 and 45, for example, are 480, 680, and 720. 360 is the least common multiple since it is the smallest.
40 and 45 have an LCM of 360.
Least Common Multiple of 40 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 40 and 45, than apply into the LCM equation.
GCF(40,45) = 5
LCM(40,45) = ( 40 × 45) / 5
LCM(40,45) = 1800 / 5
LCM(40,45) = 360
Related Least Common Multiples of 40
Related Least Common Multiples of 45
Frequently Asked Questions on LCM of 40 and 45
1. What is the LCM of 40 and 45?
The LCM of 40 and 45 is 360.
2. How to find the lowest common multiple of 40 and 45?
To find the lowest common multiple of 40 and 45, we have to get the multip;es of both numbers and identify the least common multiple in them which is 360.
3. What are the Factors of 40?
Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.
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 40 and 45?Answer:
Least Common Multiple of 40 and 45 = 360
Step 1: Find the prime factorization of 40
40 = 2 x 2 x 2 x 5
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 = 360 = 2 x 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 40 and 45 is 360.