A math game is introduced in a school competition to test the skills of students. The game deals with Prime numbers.The game rules are as follows:From the given set of distinct natural numbers as input, consider the smallest natural number as q.Your task is to compute the smallest prime number (p) such that when p is divided by all the distinct numbers in the input, except q, should result q as the remainder.Constraints1 < n < 11p < 10 ^ 10

PrimeConstructionMarks: 30Problem DescriptionA math game is introduced in a school competition to test the skills of students. The game deals with Prime numbers.The game rules are as follows:From the given set of distinct natural numbers as input, consider the smallest natural number as q.Your task is to compute the smallest prime number (p) such that when p is divided by all the distinct numbers in the input, except q, should result q as the remainder.Constraints1 < n < 11p < 10 ^ 10InputInput consists of n+1 number of distinct natural numbers separated by spaces.OutputPrint single integer p if such a p exists, else print "None".Time Limit (secs)1ExamplesInput3 4 5 1Output61ExplanationHere the n+1 numbers are 3, 4, 5 and 1 where q=1 (the least of the numbers)The smallest number that leaves remainder 1 when divided by 3, 4 and 5 is 61 and is prime. Hence, output is 61.Example 2Input3 4 5 2OutputNoneExplanationHere q=2. Any number that when divided by 4 leaving remainder 2 must be an even number e.g., 6, 10, 14 etc. Hence it can't be prime. Hence, output is "None"

Problem StatementNaveen is tasked with a mathematical challenge that requires finding the smallest positive number that is evenly divisible by all integers from 1 to a given positive number, 'n' received as input from the user. In simpler terms, find the smallest number that can be divided by all whole numbers from 1 up to 'n' without any remainder. Make sure to employ the break statement to ensure efficiency in the program.ExampleInput: 10Output: 2520Explanation: Start with the prime factorization of each number from 1 to 10:1 = 12 = 23 = 34 = 2 * 25 = 56 = 2 * 37 = 78 = 2 * 2 * 29 = 3 * 310 = 2 * 5Identify the maximum power of each prime factor:23 (from 8)32 (from 9)5 (from 5)7 (from 7)Multiply these together:23 * 32 * 5 * 7 = 2520.So, 2520 is the smallest number that can be evenly divided by all the whole numbers from 1 to 10.Note: This question helps in clearing the AMCAT exam.Input format :The input consists of a single integer n.Output format :The output displays the smallest positive number that is divisible by all integers from 1 to n without leaving any remainder.Refer to the sample output for the formatting specifications.Code constraints :In the given scenario, the test cases fall under the following constraints:2 ≤ n ≤ 20Sample test cases :Input 1 :10Output 1 :2520Input 2 :2Output 2 :2Input 3 :20Output 3 :232792560

Problem statementSend feedbackYou are given a positive integer ‘N’. Your task is to print all prime numbers less than or equal to N.Note: A prime number is a natural number that is divisible only by 1 and itself. Example - 2, 3, 17, etc.You can assume that the value of N will always be greater than 1. So, the answer will always exist.Detailed explanation ( Input/output format, Notes, Images )Constraints:2 <= N <= 10^7Where ‘N’ is the given positive integer.Time Limit: 1secSample Input 1 :7Sample Output 1 :2 3 5 7Sample Output 1 Explanation:For the given input, all prime numbers from 2 to 7 are 2, 3, 5 and 7.Sample Input 2 :30Sample Output 2 :2 3 5 7 11 13 17 19 23 29

Add a functionint nextPrime(int n);that returns the smallest prime greater than n.For example:nextPrime(14) == 17nextPrime(17) == 19Change the main function to test the new code.

Define a class, and in the main() method of the class ask the user for an integer input. Based on the input, the method must print out all the prime numbers less than that number.Note: a prime number is one which is only divisible by 1 and itself.