Question

The greatest number of four digits which is divisible by 15, 25, 40, and 75 is:

• A. 9,000
• B. 9,400
• C. 9,600
• D. 9,800

Hint:

To find the highest number divisible by several numbers, calculate the LCM and then find the largest multiple within the desired range.

Answer 1

The Correct Option is C

Step 1: Find the least common multiple (LCM) of the divisors.
Divisors: 15, 25, 40, 75. LCM of 15, 25, 40, and 75 = 600

Step 2: Determine the largest four-digit number divisible by the LCM.
The largest four-digit number = 9999 \[ \text{Largest multiple} = \left\lfloor \frac{9999}{600} \right\rfloor \times 600 = 9600 \]