LCM of 75 and 83
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 75 and 83 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 6225 as output. Here you can check the answer for Find the LCM of 75 and 83.
What is LCM of 75 and 83
Given Numbers are 75, 83
We can find the LCM of 75, 83 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 75 and 83
Multiples of 75 =75,150,225,300,375,450,525,600,675,750,825,900,975,1050,1125,1200,1275,
Multiples of 83 =83,166,249,332,415,498,581,664,747,830,913,996,1079,1162,1245,1328,1411,
Now, get the least common multiple of 75, 83 which is 6225
So, the LCM of 75, 83 is 6225.
Least Common Multiple (LCM) of 75 and 83 with the help of Prime Factorisation
One method for determining the LCM of 75 and 83 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 83's prime factorization:
| 83 | 83 |
| 1 |
Prime factors of 83 are 83.
83 = 831
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: 3,5,83
.31×52×831 = 6225
This shows that the LCM of 75 and 83 is 6225.
How to Calculate the LCM of 75 and 83 Using Common Multiples
The first step in determining the Least Common Multiple of 75 and 83 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 75 and 83:
Lets look at the first ten multiples of these numbers, 75 and 83:
75,150,225,300,375,450,525,600,675,1275 are the first ten multiples of 75.
83,166,249,332,415,498,581,664,747,1411 are the first ten multiples of 83.
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 83, for example, are 900, 1275, and 1328. 6225 is the least common multiple since it is the smallest.
75 and 83 have an LCM of 6225.
Least Common Multiple of 75 and 83 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 83, than apply into the LCM equation.
GCF(75,83) = 1
LCM(75,83) = ( 75 × 83) / 1
LCM(75,83) = 6225 / 1
LCM(75,83) = 6225
Related Least Common Multiples of 75
Related Least Common Multiples of 83
Frequently Asked Questions on LCM of 75 and 83
1. What is the LCM of 75 and 83?
The LCM of 75 and 83 is 6225.
2. How to find the lowest common multiple of 75 and 83?
To find the lowest common multiple of 75 and 83, we have to get the multip;es of both numbers and identify the least common multiple in them which is 6225.
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 83?
Answer: Factors of 83 are 1, 83. There are 2 integers that are factors of 83. The greatest factor of 83 is 83.
5. How to Find the LCM of 75 and 83?Answer:
Least Common Multiple of 75 and 83 = 6225
Step 1: Find the prime factorization of 75
75 = 3 x 5 x 5
Step 2: Find the prime factorization of 83
83 = 83
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6225 = 3 x 5 x 5 x 83
Step 4: Therefore, the least common multiple of 75 and 83 is 6225.