Step 1: Understand what is being asked.
We need the smallest 5-digit number divisible by both 24 and 36. Instead of rounding up a division, let us find the remainder when 10000 is divided by the L.C.M, and add just enough to clear it.
Step 2: Find the L.C.M. of 24 and 36.
\[ 24 = 2^3\times 3, \quad 36 = 2^2\times 3^2 \]
\[ \text{L.C.M.} = 2^3\times 3^2 = 8\times 9 = 72 \]
Step 3: Divide the smallest 5-digit number by the L.C.M. and find the remainder.
The smallest 5-digit number is 10000. Divide it by 72:
\[ 10000 = 72\times 138 + r \]
Compute $72\times 138 = 9936$, so:
\[ r = 10000-9936 = 64 \]
Step 4: Add the amount needed to reach the next exact multiple of 72.
Since 10000 is 64 more than a multiple of 72, we need $72-64=8$ more to reach the very next multiple:
\[ 10000+8 = 10008 \]
Check: $10008\div 72 = 139$ exactly, confirming it is a clean multiple.
Final Answer:
The smallest 5-digit number divisible by 24 and 36 is 10008, matching option (A).
\[ \boxed{10008} \]