What is the smallest number which on subtracting 9 from it becomes divisible by 24, 33, 42 and 56?
What is the smallest number which on subtracting 9 from it becomes divisible by 24, 33, 42 and 56?
वह सबसे छोटी संख्या कौन – सी है जिसमें से 9 घटाए जाने पर वह 24, 33, 42 और 56 से विभाज्य हो जाती हैं?
Detailed Solution & Logic
Correct Answer:
1,857
Solution:
We need the smallest number such that
(number − 9) is divisible by 24, 33, 42, and 56.
Step 1: Find LCM of 24, 33, 42, 56
Prime factors:
24 = $2^3 \times 3$
33 = $3 \times 11$
42 = $2 \times 3 \times 7$
56 = $2^3 \times 7$
LCM = $2^3 \times 3 \times 7 \times 11 = 1848$
Step 2: Required number
Number = $1848 + 9 = 1857$
✅ Final Answer: 1,857
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