Python Practice With Project Euler

I recently learned Python through the website Codecademy.  This is a great way to learn a new language with many exercises to do and projects at the end of each lesson, but I needed more.  So I looked back to Project Euler.  I have tried some of the challenges featured on Project Euler using C and C++ for some challenges this works very well others however I run into issues with precision/overflow to counteract this I could research how variable precision works, then implement it in C/C++ and then finally get to the original problem.  This would be a great opportunity to learn variable precision or I could get familiar with a new language in this case I chose to become more familiar with Python.

One of the problems I did was challenge number 4: Find the largest palindrome made from the product of two 3-digit numbers. Here is my solution.

def is_num_palindrome(num):
    string = str(num)
    if string == string[::-1]:
        return True
    else:
        return False

def find_palindrome_product():
    list = []
    for i in range(100,1000):
        for j in range(i,1000):
            num = i * j
            if is_num_palindrome(num) == True:
                list.append(i * j)

    return max(list)

I then have to just call find_palindrome_product and it will give me a list of all the palindrome numbers that can be made from multiplying 3 digits together.  This one can be done in C/C++ but python makes the solution compact and elegant such as being able to convert the number to a string and then check if it is a palindrome in one line.

I also did challenge number 5 which is: What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

def smallest_multiple():
    i = 21
    while True:
        for j in reversed(xrange(1,20)):
            if i % j != 0:
                break
        else:
            return i

        i += 1

This solution took me a few tries, I had the solution from the beginning but it took a while to run so I tried optimizing it a bit. My optimization was start the loop that checks if it is evenly divisible from 20 and work down to 1 because odds are it will fail at the upper range rather than the lower range. This helped the speed out a bit.  I am going to continue to do challenges on Project Euler I hope to become much more familiar with Python by the end of it.