# Java Program for nth multiple of a number in Fibonacci Series

Given two integers n and k. Find position the n’th multiple of K in the Fibonacci series.
Examples:

```Input : k = 2, n = 3
Output : 9
3'rd multiple of 2 in Fibonacci Series is 34
which appears at position 9.

Input  : k = 4, n = 5
Output : 30
5'th multiple of 5 in Fibonacci Series is 832040
which appears at position 30.```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

An Efficient Solution is based on below interesting property.
Fibonacci series is always periodic under modular representation. Below are examples.

```F (mod 2) = 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0
Here 0 is repeating at every 3rd index and
the cycle repeats at every 3rd index.

F (mod 3) = 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2
Here 0 is repeating at every 4th index and
the cycle repeats at every 8th index.

F (mod 4) = 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3,
1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 3, 1, 0
Here 0 is repeating at every 6th index and
the cycle repeats at every 6th index.

F (mod 5) = 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0,
2, 2, 4, 1, 0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0
Here 0 is repeating at every 5th index and
the cycle repeats at every 20th index.

F (mod 6) = 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4,
3, 1, 4, 5, 3, 2, 5, 1, 0, 1, 1, 2, 3, 5, 2
Here 0 is repeating at every 12th index and
the cycle repeats at every 24th index.

F (mod 7) = 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6, 1,
0, 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6
Here 0 is repeating at every 8th index and
the cycle repeats at every 16th index.

F (mod 8) = 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2,
3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0
Here 0 is repeating at every 6th index and
the cycle repeats at every 12th index.

F (mod 9) = 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 0, 8, 8, 7,
6, 4, 1, 5, 6, 2, 8, 1, 0, 1, 1, 2, 3, 5, 8
Here 0 is repeating at every 12th index and
the cycle repeats at every 24th index.

F (mod 10) = 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0,
7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0.
Here 0 is repeating at every 15th index and
the cycle repeats at every 60th index.
```

 `// Java Program to find position of n'th multiple ` `// of a mumber k in Fibonacci Series ` `package` `gfg; ` `public` `class` `GFG { ` `    ``public` `static` `int` `findPosition(``int` `k, ``int` `n) ` `    ``{ ` `        ``long` `f1 = ``0``, f2 = ``1``, f3; ` `        ``int` `i = ``2``; ` ` `  `        ``while` `(i != ``0``) { ` `            ``f3 = f1 + f2; ` `            ``f1 = f2; ` `            ``f2 = f3; ` ` `  `            ``if` `(f2 % k == ``0``) { ` `                ``return` `n * i; ` `            ``} ` ` `  `            ``i++; ` `        ``} ` `        ``return` `0``; ` `    ``} ` ` `  `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``// Multiple no. ` `        ``int` `n = ``5``; ` ` `  `        ``// Number of whose multiple we are finding ` `        ``int` `k = ``4``; ` ` `  `        ``System.out.print(``"Position of n'th multiple"` `+ ` `                         ``" of k in Fibonacci Series is "``); ` ` `  `        ``System.out.println(findPosition(k, n)); ` `    ``} ` `} ` ` `  `// Code contributed by Mohit Gupta_OMG `

Output:

```
```

Please refer complete article on n’th multiple of a number in Fibonacci Series for more details!

My Personal Notes arrow_drop_up
Article Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.