In this article, we are going to discuss how to print all the numbers that are divisible by 3 and 5. We will write a program for finding out those numbers. For this, we can use loop or conditional statements.
Example:
Input: 75
Output: 0, 15, 30, 45, 60, 75
Input: 150
Output: 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150
We can solve this by using the following methods:
- Using for loop
- Using LCM method
- Using the arithmetic series formula
Approach 1: Using for Loop
Using n = 50 as an example, the program should output all numbers below 50 that are divisible by both 3 and 5. To do this, divide each number between 0 and n by 3 and 5 in a for loop. Print that value if the remainder in both scenarios is 0.
Example: This example describes how can we print numbers that are divisible by 3 and 5 using a for loop.
Javascript
// Function for finding out // the numbers which are // divisible by 3 and 5 function divisibleBy3and5(n) { for (let i = 0; i <= n; i++) { if (i % 3 == 0 && i % 5 == 0) { console.log(i) } } } let N = 50; // Calling function for printing // the numbers divisibleBy3and5(N); |
0 15 30 45
Time Complexity: It is taking O(N) time as for loop will iterate n (given number) times.
Auxiliary Space: The space complexity of the above code is O(1), as no extra space is required in order to complete the operation.
Approach 2: Using LCM Method
Here we are taking LCM of 3 anad 5 which is 15. If any number which is divisible by 15 it means it can also divisible by 3 and 5 so we are only searching for that number which is divisible by 15 and printing that number only.
Example: This example is showing how can you print number which are divisible by 3 and 5 using LCM
Javascript
// Creating variable having // value 50 let n = 50; // For loop for printing // numbers which are divisible // by both 3 and 5 for (let i = 0; i <= 50; i++) { // Lcm of 3 and 5 is 15 if (i % 15 == 0) { console.log(i); } } |
0 15 30 45
Time Complexity: The time complexity will be O(n) as loop will iterate n times.
Auxiliary Space: The space complexity of the above code is O(1), as no extra space is required in order to complete the operation.
Approach 3: Using the Arithmetic Series Formula
In this approach, we are going to iterate everytime with the increment of 15, as 15 is the LCM of 3 and 5, And if number is divisible by 15 then it will also be divisible by 3 and 5. And it will only work if we are starting our iteration from 0.
Example: This example describes how you can find out the numbers which are divisible by 3 and 5 using arithmetic series formula
Javascript
// JavaScript program to print // numbers that are divisible // by 3 and 5 // Lcm of 3 and 5 is 15 // LCM(3, 5) = 15 let n = 150; // Function for finding // out divisible number function divisibility(n) { // Start loop from 0 to n // by increment of +15 every time for (let i = 0; i <= n; i += 15) { console.log(i); } } // Calling function divisibility divisibility(n); |
0 15 30 45 60 75 90 105 120 135 150
Time Complexity: The time complexity will be O(n) as loop will iterate n times.
Auxiliary Space: The space complexity of the above code is O(1), as no extra space is required in order to complete the operation.
