If we list all the natural numbers below 20 that are multiples of 7 or 11, we get 7, 11 and 14. the sum of these multiples is 32. what is the sum of all the multiples of 7 or 11 up to and including 1337?

Number of multiples of 7 up to 1337:
Number of multiples of 11 up to 1337:
Number of multiples of 77 up to 1337:

This means there are distinct multiples of 7 *or* 11 up to 1337.

The sum of these multiples is



which can be computed using the well-known formula,



So you have