Skip to main content

Problem 5 Project euler solution with python

Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

 To be simple the question asked was to find the LCM(Least Common multiple) of numbers from 1 to 20.

 If we use Common Factors Grid method to find the value manually on paper, it can easily be found out.

 But to write a program to find the LCM of two or more numbers you should be knowing Euclid Algorithm. But Euclid Theorem was designed for only two numbers. Let us assume that we will have to find LCM of 3 numbers n1,n2,n3. As LCM is both assertive and commutative we can write LCM(n1,n2,n3) = LCM(LCM(n1,n2),n3). This is what I have used in the program.

 Also if you don't know what Euclid Algorithm is then Please check out Wikihow - Ways to Find the LCM of two numbers.

Program

So the program which I wrote is as follows:
The program is fast and it just took me 5.19752502441e-05 seconds.
I think this program is pretty simple and there is nothing to explain. So I am not explaining anything.
One thing I want to mention is the possibility to use the reduce function. Instead of using for loop on line31, you can use reduce function.
If you want to download the program then you can download it from Github Gist

Output


Summary

Solving this problem on paper was easy. But converting it to a program took some time for me. I think this problem was easy if you knew Euclid Algorithm, which was not so in my case. So I had to understand the concepts behind the algorithm and this problem became easy for me.

 I would like to thank the StackOverflow community and Wikihow which helped me framing the program for this problem.
Least common multiples of 3 or more
How to find the Largest Common multiple of two numbers

 Finally as all the code is neatly commented I have not explained anything. But if you have any doubt or didn't understand anything, please do comment in the comment box below and I will be glad to help you. 

 Please don't hesitate to comment if you want me to add any extra thing or if I have made any typo. 

 You can also contact me if you want to.

 Thank you. Have a nice day☺️.
Labels:

Popular posts from this blog

Project Euler Problem 67 Solution with Python

Maximum path sum II By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.
Read more

Problem 43 Project Euler Solution with python

Sub-string divisibility The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property. Let d 1 be the 1 st digit, d 2 be the 2 nd digit, and so on. In this way, we note the following: d 2 d 3 d 4 =406 is divisible by 2 d 3 d 4 d 5 =063 is divisible by 3 d 4 d 5 d 6 =635 is divisible by 5 d 5 d 6 d 7 =357 is divisible by 7 d 6 d 7 d 8 =572 is divisible by 11 d 7 d 8 d 9 =728 is divisible by 13 d 8 d 9 d 10 =289 is divisible by 17 Find the sum of all 0 to 9 pandigital numbers with this property. One might write a simple solution using direct if else statements for this problem. Using if else statements, the execution time may be a few seconds. But this is not a very good approach. I too had written a program with if else statement which will take each and every permutation of the 0-9 Pandigital and check for the conditions given in the qu...
Read more

Add/Embed SVG to Blogger website

In this post I will tell you my method(trick) of adding SVG images in a blogger website or blog. Before starting , the first thin g I am assu m ing is that you are aware of SVG if you are here. If not please see S calable V ec tor G raphics Recently when I tried to embed a SVG image for a post on pygal, I tried uploading the SVG file and blogger Image uploader came up with an error, because of which I had to find some other way.  SVG File upload Error in Blogger  I started sea rc hing Google " Embed SVG in Blogger " . I found blogorrhea , w h ich gave some i nformatio n on add ing SVG directly as a markup , which worked , but I faced another problem using this . Also th is guy has used lot of Javascript which was confusin g for me, being new to using SVG.   So I first t houg ht of learning on h ow to embed SVG in HTML and t his on e worked out. Actually we can embed SVG in HTML i n following ways: Using Object tag Using Iframe tag Using embed...
Read more