Given two integers and . The task is to find the Nth term which is divisible by either of or .
Input : a = 2, b = 5, N = 10 Output : 16 Input : a = 3, b = 7, N = 25 Output : 57
Naive Approach : A simple approach is to traverse over all the terms starting from 1 until we find the desired Nth term which is divisible by either of or . This solution has time complexity of O(N).
Efficient Approach : The idea is to use Binary search. Here we can calculate how many numbers from 1 to are divisible by either a or b by using formula:
All the multiples of lcm(a, b) will be divisible by both and so we need to remove these terms. Now if the number of divisible terms is less than N we will increase the low position of binary search otherwise decrease high until number of divisible terms is equal to N.
Below is the implementation of the above idea :
- Find the Nth term divisible by a or b or c
- Program to print all the numbers divisible by 3 and 5 for a given number
- Find the number closest to n and divisible by m
- Find an array element such that all elements are divisible by it
- Find the first natural number whose factorial is divisible by x
- Find set of m-elements with difference of any two elements is divisible by k
- Program to find GCD or HCF of two numbers
- Program to find LCM of two numbers
- Program to find LCM of 2 numbers without using GCD
- Program to find HCF iteratively
- Program to find LCM of two Fibonnaci Numbers
- Program to find largest element in an array
- Program to find GCD of floating point numbers
- Program to find the minimum (or maximum) element of an array
- Program to find remainder when large number is divided by 11
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