Which is the largest five-digit number that is completely divisible by 8, 15, 16, 21, and 5?

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