Question : Which of the following is the greatest four-digit number that is divisible by 15, 25, 40, and 75?
Option 1: 9200
Option 2: 9500
Option 3: 9600
Option 4: 9000
Correct Answer: 9600
Solution :
Given numbers = 15, 25, 40, and 75
15 = 3 × 5
25 = 5 × 5
40 = 2 × 2 × 2 × 5
75 = 3 × 5 × 5
$\therefore$ LCM of 15, 25, 40 and 75 = 3 × 5 × 5 ×2 × 2 × 2 = 600
The greatest four-digit number = 9999
When 9999 is divided by 600, then the remainder is 399.
So, the required greatest four-digit number which is divisible by 15, 25, 40, and 75 = 9999 – 399 = 9600
Hence, the correct answer is 9600.
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