Using formula for sum of first n natural numbers: S = n(n+1)/2 where n=99. S = 99(100)/2 = 9900/2 = 4950.

For divisibility by both 6 and 8, the number must be divisible by LCM(6,8) = 24. Check: 48 ÷ 24 = 2 ✓. Option A is correct.

Using the formula: HCF × LCM = Product of two numbers. Therefore, 13 × LCM = 2028. LCM = 2028 ÷ 13 = 156.

Let the number be x. According to problem: 3x - 4 = 17. Therefore, 3x = 21, x = 7.

Let the three consecutive odd numbers be (x-2), x, and (x+2). Their sum: (x-2) + x + (x+2) = 51, so 3x = 51, x = 17.

All prime numbers greater than 2 are odd because even numbers greater than 2 are divisible by 2 and hence not prime.

2^5 = 2×2×2×2×2 = 32. Therefore, x = 5.

Prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, 19. Sum = 2+3+5+7+11+13+17+19 = 77.

Since 9 and 16 are coprime (GCD = 1), LCM(9,16) = 9×16 = 144. Any number divisible by both must be divisible by 144.

Smallest 3-digit number divisible by 11: 110 (11×10). Largest 3-digit number divisible by 11: 990 (11×90). Difference = 990 - 110 = 880. Note: Rechecking, 99÷11=9, so 11×9=99 (2-digit). 11×10=110. 11×90=990. Difference = 880. Closest answer is 989.