Multiples of 2 and 7

Problem 1

If we list all the natural numbers below 50 that are multiples of 2 and 7, we get 14, 28, and 42. The sum of these multiples is 84.

Find the sum of all the multiples of 2 and 7 below 10000.


Odd 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 3 million, find the sum of all odd-valued terms that are also multiples of 7.


Smallest multiple

Problem 3

60 is the smallest number that can be divided by each of the numbers from 1 to 5 without any remainder.

What is the smallest positive number that can be divided, without any remainder, by all of the numbers from 1 to 20?


Largest palindrome product

Problem 4

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.