Which is the largest five-digit number that is completely divisible by 8, 15, 16, 21, and 5?
Which is the largest five-digit number that is completely divisible by 8, 15, 16, 21, and 5?
8, 15, 16, 21 और 5 से पूरी तरह से विभाज्य होने वाली सबसे बड़ी पांच-अंकीय संख्या निम्न में से कौन-सी है ?
Detailed Solution & Logic
Correct Answer:
99120
Step 1: Find LCM
Prime factors:
- $8 = 2^3$
- $15 = 3 \times 5$
- $16 = 2^4$
- $21 = 3 \times 7$
- $5 = 5$
LCM = $2^4 \times 3 \times 5 \times 7 = 16 \times 105 = 1680$
Step 2: Find largest 5-digit multiple of 1680
Largest 5-digit number = 99999
Now divide:
$99999 \div 1680 \approx 59.52$
So take integer part = 59
Step 3: Multiply
$1680 \times 59 = 99120$
Final Answer: 99120
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