Project Euler Solutions (Python) 1-5

Problem #1:

Multiples of 3 and 5

Problem 1

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

Solution in Python:
First Cut:


The code in both if and else block is repeated, on conjoining the two.On removing the repetition -

Problem #2:

Even Fibonacci numbers

Problem 2

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Here is the self-explanatory code:

Problem #3:

Largest prime factor

Problem 3

The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?

Here is the code, we end at sqrt of number.

Problem #4:

Largest palindrome product

Problem 4

Published on Friday, 16th November 2001, 06:00 pm; Solved by 207294

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99.
Find the largest palindrome made from the product of two 3-digit numbers.

Problem #5:

Smallest multiple

Problem 5

Published on Friday, 30th November 2001, 06:00 pm; Solved by 220723

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?

The problem calls for calculating the LCM of all values in the range 1 to 20. Let's re-use the following gcd and lcm definitions.

The entire solution would be