Question

By what smallest number must 5400 be multiplied to make it a perfect cube?

Answer 1

by factorizing 5400, we get

2×2×2×3×3×3×5×5

logic is, to become a cube, all number should be in pair in three”s

here 2 is in pair, 3 is in pair, 5 can be in pair if multiplied by one more 5

after multiplying 5, it becomes,

2×2×2×3×3×3×5×5×5

hence it is the cube of 2×3×5= 30