Generalized Approach

Limit:ab

We could further generalize this to any pair of numbers $a$ and $b$, finding the sum of their multiples that are less than $n$. Rather than knowing in advance to loop every 15, we need to find the Least Common Multiple of the pair and use that as our row size. We can compute it with Euclid's algorithm (which actually determines the greatest common divisor, which we then easily derive the LCM from).

function SumOfPairsLessThan(a: number, b: number, n: number): number {
  const width = lcm(a, b);
  const k = Math.floor(n / width);
  const diva = width / a;
  const divb = width / b;

  const rowcount = diva + divb - 1;
  const rowsum = (diva * (diva + 1) * a + divb * (divb + 1) * b) / 2;

  var sum = rowcount * width * k * (k - 1) / 2;
  sum += k * rowsum;

  const delta = n - 1 - k*width;
  const rema = delta / a;
  const remb = delta / b;
  sum += k * width * (rema + remb + 1);
  sum += rema * (rema + 1) * a / 2;
  sum += remb * (remb + 1) * b / 2;

  return sum
}

function lcm(a: number, b: number): number {
  // Javascript and floating-point error, let's round to be sure, though it's
  // only needed when a*b is many orders of magnitude larger than gcd(a, b).
  return Math.round((a * b) / gcd(a, b));
}

function gcd(a: number, b: number): number {
  if (b === 0) {
    return a;
  }
  return gcd(b, a % b);
}