LCM of 75 and 80
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 75 and 80 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1200 as output. Here you can check the answer for Find the LCM of 75 and 80.
What is LCM of 75 and 80
Given Numbers are 75, 80
We can find the LCM of 75, 80 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 75 and 80
Multiples of 75 =75,150,225,300,375,450,525,600,675,750,825,900,975,1050,1125,1200,1275,
Multiples of 80 =80,160,240,320,400,480,560,640,720,800,880,960,1040,1120,1200,1280,1360,
Now, get the least common multiple of 75, 80 which is 1200
So, the LCM of 75, 80 is 1200.
Least Common Multiple (LCM) of 75 and 80 with the help of Prime Factorisation
One method for determining the LCM of 75 and 80 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 75's prime factorization:
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 75 are 3,5.
75 = 31×52
And this is 80's prime factorization:
| 2 | 80 |
| 2 | 40 |
| 2 | 20 |
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 80 are 2,5.
80 = 24×51
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
.24×31×52 = 1200
This shows that the LCM of 75 and 80 is 1200.
How to Calculate the LCM of 75 and 80 Using Common Multiples
The first step in determining the Least Common Multiple of 75 and 80 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 75 and 80:
Lets look at the first ten multiples of these numbers, 75 and 80:
75,150,225,300,375,450,525,600,675,1275 are the first ten multiples of 75.
80,160,240,320,400,480,560,640,720,1360 are the first ten multiples of 80.
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 75 and 80, for example, are 900, 1275, and 1280. 1200 is the least common multiple since it is the smallest.
75 and 80 have an LCM of 1200.
Least Common Multiple of 75 and 80 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75 and 80, than apply into the LCM equation.
GCF(75,80) = 5
LCM(75,80) = ( 75 × 80) / 5
LCM(75,80) = 6000 / 5
LCM(75,80) = 1200
Related Least Common Multiples of 75
Related Least Common Multiples of 80
Frequently Asked Questions on LCM of 75 and 80
1. What is the LCM of 75 and 80?
The LCM of 75 and 80 is 1200.
2. How to find the lowest common multiple of 75 and 80?
To find the lowest common multiple of 75 and 80, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1200.
3. What are the Factors of 75?
Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.
4. What are the Factors of 80?
Answer: Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. There are 10 integers that are factors of 80. The greatest factor of 80 is 80.
5. How to Find the LCM of 75 and 80?Answer:
Least Common Multiple of 75 and 80 = 1200
Step 1: Find the prime factorization of 75
75 = 3 x 5 x 5
Step 2: Find the prime factorization of 80
80 = 2 x 2 x 2 x 2 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 = 1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 75 and 80 is 1200.