correct answer is: a) 99960.

Explanation

1^st we need to find the LCM of 2,3,4,5,6 and 7.
So that, the LCM of 2,3,4,5,6 and 7 is:
\rightarrow 2\times2\times3\times5\times7=420
Now we divide 100000 by the LCM of 420.
\rightarrow\left(100000\div420\right) = 238 quotient and 40 remainder.
Now, \left(100000-40\right)=99960
\therefore 99960 is the one nearer to 100000 which is exactly divisible by 2,3,4,5,6 and 7.

And 100000+\left(420-40\right)=100000+380
\rightarrow 100380
\therefore 100380 is the another nearer to 100000 which is exactly divisible by 2,3,4,5,6 and 7.
So that, between these two number 99960 is nearer to 100000.
\therefore 99960 is the required nearer number which is exactly divisible by 2,3,4,5,6 and 7.
Ans: 99960.

An alternative way to phrase this math particular query is possible:

1. Find the number nearest to 100,000 that is exactly divisible by 2, 3, 4, 5, 6, and 7.
2. What is the nearest multiple of 2, 3, 4, 5, 6, and 7 to 100,000?
3. Identify the number closest to 100,000 that is divisible by 2, 3, 4, 5, 6, and 7.
4. If a number is to be divisible by 2, 3, 4, 5, 6, and 7, what is the nearest such number to 100,000?