Problem 5
Determine the largest integer n with the property that n is divisible by every positive integer less than the cube root of n.
Step 1 of 4: Verify the candidate 420
Detailed analysis
The positive integers below the cube root of 420 are 1 through 7, and 420 is divisible by all of them. The next relevant test is 840: its cube root is greater than 9, but 840 is not divisible by 9, so the largest value, if finite, is plausibly 420.