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We can begin by making each fraction have a common denominator:
If we make each have a common denominator of ab, we get:
Simplify:
Multiply both sides by ab:
Move b to the opposite side:
Factor out b:
Divide by (ac - 1):
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Let the least possible value of the smallest of 99 cosecutive integers be x and let the number whose cube is the sum be p, then
By substitution, we have that
and 
.
Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>
By substitution, we have that
Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>