The question is a bit ambiguous. Let's interpret it in a couple of ways and provide answers for each interpretation.
Interpretation 1: Largest Number Divisible by a Set of Given Numbers
This interpretation assumes we have a set of numbers, and we want to find the largest number (within a certain range, implicitly) that is divisible by all of them. A common scenario is finding the largest n-digit number divisible by a set of numbers.
Process:
- Find the Least Common Multiple (LCM): Calculate the LCM of the given set of numbers. The LCM is the smallest number that is divisible by each number in the set.
- Determine the Range (Optional): If you're looking for the largest number within a specific range (e.g., the largest 4-digit number), define the upper bound of that range. If not, you're basically looking for infinity (there is no 'largest' number, as numbers go on forever).
- Divide and Conquer: Divide the upper bound of the range (or a very large number if no specific range is provided) by the LCM.
- Multiply to Find the Largest Divisible Number: Multiply the whole number part of the result from step 3 by the LCM. This yields the largest number within the specified range (or, close to your test number) that is divisible by all the numbers in the original set.
- Verification: Check if the answer is correct by dividing the result by all the given numbers. All the divisions should give a whole number as the result.
Example (Based on Vedantu reference):
Find the largest 4-digit number exactly divisible by 12, 15, and 18.
- Find the LCM: The LCM of 12, 15, and 18 is 180. (You can find this by prime factorization or other methods).
- Range: We're looking for a number less than or equal to 9999 (the largest 4-digit number).
- Divide: 9999 / 180 = 55.55
- Multiply: 55 * 180 = 9900
- Verification: 9900/12 = 825; 9900/15 = 660; 9900/18 = 550. 9900 is indeed divisible by each.
Therefore, the largest 4-digit number divisible by 12, 15, and 18 is 9900.
Interpretation 2: Largest Number Divisible By Any Number
This is a trickier interpretation. If we interpret "any number" as meaning every possible number, then the only number divisible by every number is zero (0).
Why?
- Any number divided by zero is undefined.
- Zero divided by any number is zero.
If, instead, the intention is to determine whether there is a general rule applicable to any number, the most appropriate action would be to determine whether the question reflects the answer and, if needed, rephrase the query.
