Question

The largest 4-digit number exactly divisible by 12, 15, 18 and 27 is

• A. 9690
• B. 9820
• C. 9720
• D. 9976

Answer 1

The correct option is C 9720

Given numbers are 12, 15, 18, 27.

The largest 4-digit number known is 9999.

For the largest number exactly divisible by 12, 15, 18 and 27, we need to find the LCM.


∴ LCM (12, 15, 18, 27) = 2 × 2 × 3 × 3 × 3 × 5 = 540

To check whether the greatest 4-digit number is divisible by 540, we must divide by 9999 by 540.

On dividing, $\frac{9999}{540}=18\frac{279}{540},\left(279\mathrm{is}\mathrm{remainder}\right)$

So, 9999 – 279 = 9720 is the largest 4-digit number divisible by 540.

Hence, the correct answer is option (c).