Determine the largest four-digit number that is exactly divisible by 15, 25, 40, and 75.

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SSC GD Constable 2025 Official Paper (Held On: 04 Feb, 2025 Shift 1)
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  1. 9600
  2. 9960
  3. 9975
  4. 9999

Answer (Detailed Solution Below)

Option 1 : 9600
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Detailed Solution

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Given:

Determine the largest four-digit number that is exactly divisible by 15, 25, 40, and 75.

Formula used:

Find the LCM of 15, 25, 40, and 75

Calculation:

Prime factorization:

15 = 3 × 5

25 = 52

40 = 23 × 5

75 = 3 × 52

LCM = 23 × 3 × 52 = 600

Largest four-digit number = 9999

⇒ 9999 ÷ 600 = 16.665

⇒ Nearest integer quotient = 16

⇒ Largest four-digit number divisible by 600 = 600 × 16 = 9600

∴ The correct answer is option 1.

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