LCM of 45 and 30
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 45 and 30 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 90 as output. Here you can check the answer for Find the LCM of 45 and 30.
What is LCM of 45 and 30
Given Numbers are 45, 30
We can find the LCM of 45, 30 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 45 and 30
Multiples of 45 =45,90,135,180,225,270,315,360,405,450,495,540,585,630,675,720,765,
Multiples of 30 =30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,
Now, get the least common multiple of 45, 30 which is 90
So, the LCM of 45, 30 is 90.
Least Common Multiple (LCM) of 45 and 30 with the help of Prime Factorisation
One method for determining the LCM of 45 and 30 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 45's prime factorization:
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 45 are 3,5.
45 = 32×51
And this is 30's prime factorization:
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 30 are 2, 3,5.
30 = 21×31×51
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: 3,5,2
.21×32×51 = 90
This shows that the LCM of 45 and 30 is 90.
How to Calculate the LCM of 45 and 30 Using Common Multiples
The first step in determining the Least Common Multiple of 45 and 30 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 45 and 30:
Lets look at the first ten multiples of these numbers, 45 and 30:
45,90,135,180,225,270,315,360,405,765 are the first ten multiples of 45.
30,60,90,120,150,180,210,240,270,510 are the first ten multiples of 30.
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 45 and 30, for example, are 540, 765, and 480. 90 is the least common multiple since it is the smallest.
45 and 30 have an LCM of 90.
Least Common Multiple of 45 and 30 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 30, than apply into the LCM equation.
GCF(45,30) = 15
LCM(45,30) = ( 45 × 30) / 15
LCM(45,30) = 1350 / 15
LCM(45,30) = 90
Related Least Common Multiples of 45
Related Least Common Multiples of 30
Frequently Asked Questions on LCM of 45 and 30
1. What is the LCM of 45 and 30?
The LCM of 45 and 30 is 90.
2. How to find the lowest common multiple of 45 and 30?
To find the lowest common multiple of 45 and 30, we have to get the multip;es of both numbers and identify the least common multiple in them which is 90.
3. 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.
4. 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.
5. How to Find the LCM of 45 and 30?Answer:
Least Common Multiple of 45 and 30 = 90
Step 1: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 2: Find the prime factorization of 30
30 = 2 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 = 90 = 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 45 and 30 is 90.