Institution: AGRANI BANK LTD Exam: Agrani bank Ltd - Senior Officer - 12.02.2010
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To determine the lowest positive integer divisible by the numbers 2, 3, 4, 5, 6, 7, 8, and 9, we need to find the least common multiple (LCM) of these numbers.

First, we break down each number into its prime factors:

- 2 = 2
- 3 = 3
- 4 = 2²
- 5 = 5
- 6 = 2 × 3
- 7 = 7
- 8 = 2³
- 9 = 3²

Next, we identify the highest powers of each prime that appear in any of the factorizations:

- The highest power of 2 is \(2^3\) (from 8).
- The highest power of 3 is \(3^2\) (from 9).
- The highest power of 5 is \(5^1\) (from 5).
- The highest power of 7 is \(7^1\) (from 7).

Now, we multiply these together to find the LCM:

\[
LCM = 2^3 \times 3^2 \times 5^1 \times 7^1 = 8 \times 9 \times 5 \times 7
\]

Calculating this step-by-step:

1. \(8 \times 9 = 72\)
2. \(72 \times 5 = 360\)
3. \(360 \times 7 = 2520\)

Thus, the least common multiple is 2520, which means it is the smallest positive integer that is divisible by all given numbers (2 to 9). Among the given options, only option B) 2,520 is correct. Options A) 15,120, C) 3,024, and D) 1,890 do not meet all divisibility requirements.