The greatest four digit number which is divisible by 18, 25, 30, and 48 is:Options :A] 9000B] 9200C] 7200D] 9729

To find the greatest four-digit number divisible by 18, 25, 30, and 48, we need to find the least common multiple (LCM) of these numbers. However, since the LCM of these numbers is likely to be a large number, we can use a shortcut by finding the LCM of the largest two numbers, 48 and 30.

The prime factors of 48 are 2, 2, 2, 2, 3 (or 2^4 * 3). The prime factors of 30 are 2, 3, 5 (or 2 * 3 * 5).

The LCM is found by multiplying the highest power of all prime numbers in the factorization of each number. So, the LCM of 48 and 30 is 2^4 * 3 * 5 = 240.

Now, we need to find the greatest four-digit number divisible by 240. To do this, we divide the greatest four-digit number, 9999, by 240.

9999 ÷ 240 = 41 remainder 159.

So, the greatest four-digit number divisible by 240 is 41 * 240 = 9840.

However, we need to check if 9840 is also divisible by 18 and 25. It turns out that 9840 is not divisible by 25. So, we need to find the next largest number that is divisible by 240 and 25.

To do this, we subtract 240 from 9840 until we find a number that is divisible by 25. This number is 9600.

So, the greatest four-digit number divisible by 18, 25, 30, and 48 is 9600. Therefore, the answer is not in the options given.