Given a number, we need to find LCM of the factorial of the numbers and its neighbors. If the number is N, we need to find LCM of (N-1)!, N! and (N+1)!.Here N is always greater than or equal too 1
Input : N = 5 Output : 720 Explanation Here the given number is 5, its neighbors are 4 and 6. The factorial of these three numbers are 24, 120, and 720.so the LCM of 24, 120, 720 is 720. Input : N = 3 Output : 24 Explanation Here the given number is 3, its Neighbors are 2 and 4.the factorial of these three numbers are 2, 6, and 24. So the LCM of 2, 6 and 24 is 24.
Method 1(Simple). We first calculate the factorial of number and and the factorial of its neighbor then
find the LCM of these factorials numbers.
We can see that the LCM of (N-1)!, N! and (N+1)! is always (N-1)! * N! * (N+1)!
this can be written as (N-1)! * N*(N-1)! * (N+1)*N*(N-1)!
so the LCM become (N-1)! * N * (N+1)
which is (N+1)!
N = 5
We need to find the LCM of 4!, 5!and 6!
LCM of 4!, 5!and 6!
= 4! * 5! * 6!
= 4! * 5*4! * 6*5*4!
So we can say that LCM of the factorial of three consecutive numbers is always the factorial of the largest number.in this case (N+1)!.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Sum of LCM(1, n), LCM(2, n), LCM(3, n), ... , LCM(n, n)
- Minimum replacement of pairs by their LCM required to reduce given array to its LCM
- Find the last digit when factorial of A divides factorial of B
- Fill array with 1's using minimum iterations of filling neighbors
- Puzzle | Neighbors in a round table
- Find N numbers such that a number and its reverse are divisible by sum of its digits
- Count of Array elements greater than all elements on its left and next K elements on its right
- Count of Array elements greater than all elements on its left and at least K elements on its right
- Smallest N digit number with none of its digits as its divisor
- Count digits in a factorial | Set 2
- Count trailing zeroes in factorial of a number
- Factorial of a large number
- Count factorial numbers in a given range
- Count digits in a factorial | Set 1
- Count Divisors of Factorial
- Find the first natural number whose factorial is divisible by x
- Smallest number with at least n trailing zeroes in factorial
- Last non-zero digit of a factorial
- Smallest number with at least n digits in factorial
- Double factorial
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.