Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197.
Let the numbers be x, x + 2, x + 4, x + 6, and x + 8Avg = x + x + 2 + x + 4 + x + 6 + x + 8/5 = 40Therefore, 5x + 20 = 200Therefore, x = 180/5 = 36Therefore, r = x + 4 = 40 s = x + 6 = 42Therefore, Product = 1680