Sum of multiples

Problem

Write a function that takes two things, in this order: a list of factors and a limit. It returns the sum of the numbers below the limit that are multiples of at least one of the factors. The limit itself is left out. A number is a multiple of another one when the division comes out even: 6 is a multiple of 3 because 6 divided by 3 gives 2 and nothing is left. The numbers you look at go from 1 up to the limit, limit not included. With factors 3 and 5 and limit 4 you look at 1, 2 and 3: the only one that is a multiple of either factor is the 3, so you return 3.

Here is the part people get wrong: a number that is a multiple of several factors is added only once. With factors 4 and 6 and limit 15 the numbers that count are 4, 6, 8 and 12. The 12 is a multiple of 4 and also of 6, but it goes in once: the total is 30, not 42.

If the list of factors comes in empty, you return 0.

A factor of 0 is ignored: it adds nothing to the sum. Skip it before dividing, because in Python dividing by 0 blows up.

Examples

• The example above

  [3, 5], 4 → 3

• Three and five up to 10

  [3, 5], 10 → 23

• No multiples at all

  [3, 5], 1 → 0

• Three factors

  [7, 13, 17], 20 → 51

• No factors

  [], 10 → 0

Besides these, the challenge has hidden tests that are revealed when you submit your solution.

You start with this

def sum_multiples(factors, limit):
    pass

function sumMultiples(factors, limit) {
}