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.

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, in this case, the LCM of these numbers is larger than 9999, which is the largest four-digit number. Therefore, we need to find the largest four-digit number that is a multiple of the LCM.

Here are the steps:

1. Find the LCM of 18, 25, 30, and 48. The LCM of these numbers is 1800.

2. Divide the largest four-digit number (9999) by the LCM (1800). The quotient is 5 and the remainder is 1999.

3. Subtract the remainder from the largest four-digit number. This gives us 8000, which is not divisible by all the given numbers.

4. Therefore, we need to subtract one more LCM from 8000. This gives us 6200, which is still not divisible by all the given numbers.

5. Subtract one more LCM from 6200. This gives us 4400, which is still not divisible by all the given numbers.

6. Subtract one more LCM from 4400. This gives us 2600, which is still not divisible by all the given numbers.

7. Subtract one more LCM from 2600. This gives us 800, which is not a four-digit number.

Therefore, the greatest four-digit number which is divisible by 18, 25, 30, and 48 is not among the options given. There seems to be a mistake in the question or the options provided.

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.

Step 1: Prime factorization of the numbers 18 = 2 * 3^2 25 = 5^2 30 = 2 * 3 * 5 48 = 2^4 * 3

Step 2: Find the LCM The LCM is the product of the highest powers of all the factors. LCM = 2^4 * 3^2 * 5^2 = 1800

Step 3: Find the greatest four-digit number divisible by the LCM The greatest four-digit number is 9999. Divide 9999 by the LCM (1800) and find the remainder.

9999 ÷ 1800 = 5 remainder 999

Subtract the remainder from 9999 to find the largest four-digit number divisible by 1800.

9999 - 999 = 9000

So, the greatest four-digit number which is divisible by 18, 25, 30, and 48 is 9000. Therefore, the answer is option A] 9000.

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.

Step 1: Prime factorization of the numbers 18 = 2 * 3^2 25 = 5^2 30 = 2 * 3 * 5 48 = 2^4 * 3

Step 2: Find the LCM The LCM is the product of the highest powers of all the factors. LCM = 2^4 * 3^2 * 5^2 = 1800

Step 3: Find the greatest four-digit number divisible by the LCM The greatest four-digit number is 9999. Divide 9999 by the LCM (1800) and find the remainder.

9999 ÷ 1800 = 5 remainder 999

Subtract the remainder from 9999 to find the greatest four-digit number divisible by 1800.

9999 - 999 = 9000

So, the greatest four-digit number divisible by 18, 25, 30, and 48 is 9000. Therefore, the answer is option A] 9000.

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 we are looking for the greatest four-digit number, we need to find the highest number below 10,000 (the smallest five-digit number) that is divisible by the LCM of 18, 25, 30, and 48.

Step 1: Find the LCM of 18, 25, 30, and 48. The LCM of 18, 25, 30, and 48 is 1800.

Step 2: Find the greatest four-digit number divisible by the LCM. To find this, divide 10,000 by the LCM and round down to the nearest whole number. Then multiply this number by the LCM.

10000 ÷ 1800 = 5.55555556 (rounded down to 5) 5 * 1800 = 9000

So, the greatest four-digit number divisible by 18, 25, 30, and 48 is 9000. Therefore, the answer is A] 9000.