What is the highest number between 5000 and 5500, which when divided by 12,16 and 24, would leave a remainder 9?

Solution / समाधान

Let the required number be $N$.

According to the question,

When $N$ is divided by 12, 16, and 24, the remainder is 9.

So,

$N - 9$ must be divisible by 12, 16, and 24.

Find the LCM of 12, 16, and 24:

$12 = 2^2 \times 3$

$16 = 2^4$

$24 = 2^3 \times 3$

Therefore,

$\text{LCM} = 2^4 \times 3 = 48$

So,

$N = 48k + 9$

Now find the greatest number between 5000 and 5500.

Largest multiple of 48 below 5500:

$48 \times 114 = 5472$

Therefore,

$N = 5472 + 9 = 5481$

Correct Answer / सही उत्तर:
5481