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
Question
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
Solution 1
The problem statement is asking to write a program that will find the smallest positive number that is evenly divisible by all integers from 1 to a given positive number 'n'. This number 'n' will be provided by the user. The program should be efficient and use the break statement.
Here is a step-by-step solution:
-
Start by initializing a variable, say
result, to 1. This will hold our final result. -
Create a loop that will run from 2 to 'n'. For each number in this range, we will find the highest power of the number that divides 'n'. This is done by repeatedly dividing 'n' by the number until 'n' is no longer divisible by the number.
-
Multiply
resultby the number raised to its highest power. This will ensure thatresultis divisible by all numbers from 1 to 'n'. -
Continue this process for all numbers from 2 to 'n'. Once the loop is finished,
resultwill be the smallest number that is divisible by all numbers from 1 to 'n'. -
Print
result.
This solution works because the smallest number that is divisible by a set of numbers is the product of the highest powers of all prime numbers within the set. By finding the highest power of each number that divides 'n', we are effectively finding the highest powers of all prime numbers that divide 'n'. Multiplying these together gives us the smallest number that is divisible by all numbers from 1 to 'n'.
Solution 2
The problem statement is asking to write a program that will find the smallest positive number that is evenly divisible by all integers from 1 to a given positive number 'n'. This number 'n' will be provided by the user. The program should be efficient and use the break statement.
Here is a step-by-step solution:
- Start by initializing a variable, say
result, to 1. This will hold our
Similar Questions
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