Question

1. find the 30th smallest multiple of 11 greater than 3,000,000

Explanation:

Step1: Find quotient and remainder

Calculate $3000000 \div 11$.
$11 \times 272727 = 2999997$, remainder $3000000 - 2999997 = 3$.

Step2: First multiple >3000000

First multiple: $11 \times (272727 + 1) = 11 \times 272728 = 3000008$.

Step3: 30th multiple

30th multiple: $3000008 + 11 \times (30 - 1) = 3000008 + 319 = 3000327$? Wait correction: Wait first multiple after 3000000 is when we add (11-3)=8 to 3000000: 3000008 (correct). Then each next multiple adds 11. So 30th multiple is first + 11(29) = 3000008 + 319 = 3000327? Wait wait 11272728=3000008 (1st), 11272729=3000019 (2nd), ..., 11(272728+29)=11272757= let's calculate 27275711: 272757*10 +272757=2727570+272757=3000327. Yes correct. So final answer 3000327. Wait earlier typo fixed.

Wait final correction: 272728 +29=272757; 272757*11=3000327. Correct.

Step1: Compute quotient and remainder

$3000000 \div 11 = 272727$ remainder $3$.

Step2: First valid multiple

First multiple >3000000: $11 \times (272727+1)=3000008$.

Step3: Calculate 30th multiple

30th multiple: $3000008 +11\times29=3000008+319=3000327$.

Answer:

3000352