To find the numbers nearest to 10,000 that are exactly divisible by 2, 3, 4, 5, 6, and 7, follow these steps:
1. Evaluate the Least Common Multiple (LCM):
- The numbers given are 2, 3, 4, 5, 6, and 7.
- The task is to find the least common multiple (LCM) of these numbers.
- The LCM is the smallest number that is a multiple of all the given numbers.
2. Identify the Target Number:
- The target number here is 10,000.
3. Calculate the Multiples:
- First, find the multiple of the LCM that is closest to but not greater than 10,000 (let's call it the lower multiple).
- Then, find the next multiple of the LCM that is greater than 10,000 (let's call it the upper multiple).
4. Determine the Nearest Multiples:
- The nearest multiple of the LCM to 10,000 will either be the lower multiple or the upper multiple.
Given the result, the nearest numbers to 10,000 that are exactly divisible by 2, 3, 4, 5, 6, and 7 are:
- The lower number: 9660
- The upper number: 10080
Therefore, the answer to the question is:
c) 9660; 10080
