LCM of 45 and 52
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 45 and 52 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2340 as output. Here you can check the answer for Find the LCM of 45 and 52.
What is LCM of 45 and 52
Given Numbers are 45, 52
We can find the LCM of 45, 52 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 45 and 52
Multiples of 45 =45,90,135,180,225,270,315,360,405,450,495,540,585,630,675,720,765,
Multiples of 52 =52,104,156,208,260,312,364,416,468,520,572,624,676,728,780,832,884,
Now, get the least common multiple of 45, 52 which is 2340
So, the LCM of 45, 52 is 2340.
Least Common Multiple (LCM) of 45 and 52 with the help of Prime Factorisation
One method for determining the LCM of 45 and 52 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 52's prime factorization:
| 2 | 52 |
| 2 | 26 |
| 13 | 13 |
| 1 |
Prime factors of 52 are 2,13.
52 = 22×131
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, 2,13
.22×32×51×131 = 2340
This shows that the LCM of 45 and 52 is 2340.
How to Calculate the LCM of 45 and 52 Using Common Multiples
The first step in determining the Least Common Multiple of 45 and 52 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 45 and 52:
Lets look at the first ten multiples of these numbers, 45 and 52:
45,90,135,180,225,270,315,360,405,765 are the first ten multiples of 45.
52,104,156,208,260,312,364,416,468,884 are the first ten multiples of 52.
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 52, for example, are 540, 765, and 832. 2340 is the least common multiple since it is the smallest.
45 and 52 have an LCM of 2340.
Least Common Multiple of 45 and 52 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 52, than apply into the LCM equation.
GCF(45,52) = 1
LCM(45,52) = ( 45 × 52) / 1
LCM(45,52) = 2340 / 1
LCM(45,52) = 2340
Related Least Common Multiples of 45
Related Least Common Multiples of 52
Frequently Asked Questions on LCM of 45 and 52
1. What is the LCM of 45 and 52?
The LCM of 45 and 52 is 2340.
2. How to find the lowest common multiple of 45 and 52?
To find the lowest common multiple of 45 and 52, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2340.
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 52?
Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.
5. How to Find the LCM of 45 and 52?Answer:
Least Common Multiple of 45 and 52 = 2340
Step 1: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 2: Find the prime factorization of 52
52 = 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2340 = 2 x 2 x 3 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 45 and 52 is 2340.