Merge pull request TheAlgorithms#277 from girijamanojkumarreddy/master

Added a Solution using Euclidean Algo

Author: harshildarji

Project Euler/Problem 05/sol2.py

@@ -0,0 +1,20 @@
+#!/bin/python3
+'''
+Problem:
+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(divisible with no remainder) by all of the numbers from 1 to N?
+'''
+
+""" Euclidean GCD Algorithm """
+def gcd(x,y):
+    return x if y==0 else gcd(y,x%y)
+
+""" Using the property lcm*gcd of two numbers = product of them """
+def lcm(x,y):
+    return (x*y)//gcd(x,y)
+
+n = int(input())
+g=1
+for i in range(1,n+1):
+    g=lcm(g,i)
+print(g)

Project Euler/Problem 9/sol2.py

@@ -0,0 +1,19 @@
+"""A Pythagorean triplet is a set of three natural numbers, for which,
+a^2+b^2=c^2
+Given N, Check if there exists any Pythagorean triplet for which a+b+c=N
+Find maximum possible value of product of a,b,c among all such Pythagorean triplets, If there is no such Pythagorean triplet print -1."""
+#!/bin/python3
+import sys
+
+product=-1
+d=0
+N = int(input())
+for a in range(1,N//3):
+    """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c """
+    b=(N*N-2*a*N)//(2*N-2*a)
+    c=N-a-b
+    if c*c==(a*a+b*b):
+        d=(a*b*c)
+        if d>=product:
+            product=d
+print(product)