Question:
Find the greatest four-digit number which is exactly divisible by 15, 24, and 36.
चार अंकों की वह सबसे बड़ी संख्या ज्ञात कीजिए जो 15, 24 और 36 से पूर्णतः विभाज्य हो।
Options:
- 9720
- 9840
- 9680
- 9900
- 9720
- 9840
- 9680
- 9900
Correct Answer: a)
Explanation:
1. Find LCM of 15, 24, and 36:
\(15 = 3 \times 5\)
\(24 = 2^3 \times 3\)
\(36 = 2^2 \times 3^2\)
\(\text{LCM} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360\).
2. The largest 4-digit number is 9999.
Divide 9999 by 360: \(9999 = 360 \times 27 + 279\).
Remainder = 279.
3. Required number = \(9999 – 279 = 9720\) (Option a).
1. 15, 24 और 36 का LCM = 360.
2. चार अंकों की सबसे बड़ी संख्या = 9999.
\(9999 \div 360 = 27\) (शेषफल = 279).
3. अभीष्ट संख्या = \(9999 – 279 = 9720\) (विकल्प a)।