You can calculate the Least Weighable Amount using the equation you have already used:

For the least weighable amount, you are calculating the "Actual Measurement" when you have the highest error and the highest percentage error.

A balance has a sensitivity of 15 milligrams. If the maximum error allowed when weighing a substance is 3 %, what is the smallest amount of substance that can be weighed using the balance?

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Percentage Error =                   Error                   x 100 %
Actual Measurement
Percentage Error =                   Error                   x 100 %
Least Weighable Amount
The sensitivity of the balance is 15 milligrams, thus "Error" is 15 milligrams.
3 =                     15                     x 100
Least Weighable Amount
Least Weighable Amount = 1500 mg
3
Least Weighable Amount = 500 mg
Checking the Answer
You can check the answer by finding the Percentage Error of the Least Weighable Amount. The Percentage Error of the Least Weighable Amount should be the same as the Percentage Error expressed in the original question.
Percentage Error =                   Error                  x 100 %
Least Weighable Amount
Percentage Error =     15     x 100 %
500
Percentage Error = 3 %          Which is the same as in the question.
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