LCM of 45 and 51
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 45 and 51 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 765 as output. Here you can check the answer for Find the LCM of 45 and 51.
What is LCM of 45 and 51
Given Numbers are 45, 51
We can find the LCM of 45, 51 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 45 and 51
Multiples of 45 =45,90,135,180,225,270,315,360,405,450,495,540,585,630,675,720,765,
Multiples of 51 =51,102,153,204,255,306,357,408,459,510,561,612,663,714,765,816,867,
Now, get the least common multiple of 45, 51 which is 765
So, the LCM of 45, 51 is 765.
Least Common Multiple (LCM) of 45 and 51 with the help of Prime Factorisation
One method for determining the LCM of 45 and 51 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 51's prime factorization:
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 51 are 3,17.
51 = 31×171
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: 3,5,17
.32×51×171 = 765
This shows that the LCM of 45 and 51 is 765.
How to Calculate the LCM of 45 and 51 Using Common Multiples
The first step in determining the Least Common Multiple of 45 and 51 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 45 and 51:
Lets look at the first ten multiples of these numbers, 45 and 51:
45,90,135,180,225,270,315,360,405,765 are the first ten multiples of 45.
51,102,153,204,255,306,357,408,459,867 are the first ten multiples of 51.
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 51, for example, are 540, 765, and 816. 765 is the least common multiple since it is the smallest.
45 and 51 have an LCM of 765.
Least Common Multiple of 45 and 51 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 51, than apply into the LCM equation.
GCF(45,51) = 3
LCM(45,51) = ( 45 × 51) / 3
LCM(45,51) = 2295 / 3
LCM(45,51) = 765
Related Least Common Multiples of 45
Related Least Common Multiples of 51
Frequently Asked Questions on LCM of 45 and 51
1. What is the LCM of 45 and 51?
The LCM of 45 and 51 is 765.
2. How to find the lowest common multiple of 45 and 51?
To find the lowest common multiple of 45 and 51, we have to get the multip;es of both numbers and identify the least common multiple in them which is 765.
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 51?
Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.
5. How to Find the LCM of 45 and 51?Answer:
Least Common Multiple of 45 and 51 = 765
Step 1: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 2: Find the prime factorization of 51
51 = 3 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 765 = 3 x 3 x 5 x 17
Step 4: Therefore, the least common multiple of 45 and 51 is 765.