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# OPSC OAS Prelims 2022 GS Paper 2 Solved Question Paper

1. Find the greatest 6- digit number among the following which is exactly divisible by 24, 15 and 36.
(A) 999999
(B) 999720
(C) 999750
(D) 999820

Ans: (B) 999720

Solution:  Find the Greatest 6-Digit Number Divisible by 24, 15, and 36

To find the greatest 6-digit number among the given options that is exactly divisible by 24, 15, and 36, we first need to determine the Least Common Multiple (LCM) of these numbers.

Step 1: Prime Factorization

$24 = 2^3 \times 3$
$15 = 3 \times 5$
$36 = 2^2 \times 3^2$

Step 2: Find the LCM

LCM is found by taking the highest powers of all prime factors:

$2^3 \quad (\text{from } 24)$
$3^2 \quad (\text{from } 36)$
$5 \quad (\text{from } 15)$
$\text{Therefore, LCM} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360$

Step 3: Check the Options

$\frac{999999}{360} = 2777.775$
This is not an integer, so 999999 is not divisible by 360.

$\frac{999720}{360} = 2777$
This is an integer, so 999720 is divisible by 360.

$\frac{999750}{360} = 2777.0833$
This is not an integer, so 999750 is not divisible by 360.

$\frac{999820}{360} = 2777.2777$
This is not an integer, so 999820 is not divisible by 360.