Find the least multiple of 23 which when divided by 24, 21, and 18 leaves the remainders 13, 10, and 7 respectivelyOptions :A] 3004B] 3024C] 3013D] 3026

To solve this problem, we need to find a number that fits all the given conditions.

Step 1: Find the least common multiple (LCM) of 24, 21, and 18. The LCM of these numbers is 504.

Step 2: The number we are looking for is a multiple of 23 and leaves a remainder of 13 when divided by 24, 10 when divided by 21, and 7 when divided by 18. This means the number is of the form 504k + 13, 504k + 10, and 504k + 7.

Step 3: To find the least such number, we can start checking from k = 1. We find that 504*1 + 13 = 517 is not divisible by 23.

Step 4: We continue this process until we find a number that is divisible by 23. We find that 5046 + 13 = 3029 is not divisible by 23, but 5046 + 10 = 3026 is divisible by 23.

So, the least multiple of 23 which when divided by 24, 21, and 18 leaves the remainders 13, 10, and 7 respectively is 3026.

Therefore, the answer is D] 3026.