LCM of 68 and 75
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 68 and 75 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5100 as output. Here you can check the answer for Find the LCM of 68 and 75.
What is LCM of 68 and 75
Given Numbers are 68, 75
We can find the LCM of 68, 75 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 68 and 75
Multiples of 68 =68,136,204,272,340,408,476,544,612,680,748,816,884,952,1020,1088,1156,
Multiples of 75 =75,150,225,300,375,450,525,600,675,750,825,900,975,1050,1125,1200,1275,
Now, get the least common multiple of 68, 75 which is 5100
So, the LCM of 68, 75 is 5100.
Least Common Multiple (LCM) of 68 and 75 with the help of Prime Factorisation
One method for determining the LCM of 68 and 75 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 68's prime factorization:
| 2 | 68 |
| 2 | 34 |
| 17 | 17 |
| 1 |
Prime factors of 68 are 2,17.
68 = 22×171
And this is 75's prime factorization:
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 75 are 3,5.
75 = 31×52
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: 2,17, 3,5
.22×31×52×171 = 5100
This shows that the LCM of 68 and 75 is 5100.
How to Calculate the LCM of 68 and 75 Using Common Multiples
The first step in determining the Least Common Multiple of 68 and 75 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 68 and 75:
Lets look at the first ten multiples of these numbers, 68 and 75:
68,136,204,272,340,408,476,544,612,1156 are the first ten multiples of 68.
75,150,225,300,375,450,525,600,675,1275 are the first ten multiples of 75.
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 68 and 75, for example, are 816, 1156, and 1200. 5100 is the least common multiple since it is the smallest.
68 and 75 have an LCM of 5100.
Least Common Multiple of 68 and 75 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68 and 75, than apply into the LCM equation.
GCF(68,75) = 1
LCM(68,75) = ( 68 × 75) / 1
LCM(68,75) = 5100 / 1
LCM(68,75) = 5100
Related Least Common Multiples of 68
Related Least Common Multiples of 75
Frequently Asked Questions on LCM of 68 and 75
1. What is the LCM of 68 and 75?
The LCM of 68 and 75 is 5100.
2. How to find the lowest common multiple of 68 and 75?
To find the lowest common multiple of 68 and 75, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5100.
3. What are the Factors of 68?
Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.
4. 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.
5. How to Find the LCM of 68 and 75?Answer:
Least Common Multiple of 68 and 75 = 5100
Step 1: Find the prime factorization of 68
68 = 2 x 2 x 17
Step 2: Find the prime factorization of 75
75 = 3 x 5 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 = 5100 = 2 x 2 x 3 x 5 x 5 x 17
Step 4: Therefore, the least common multiple of 68 and 75 is 5100.