Question

find the smallest number which when multiplied with 137592 will make the product a perfect cube​

Answer 1

1183

here it is clear that when we multiply 137592 by the number 7 × 13² we get, 2³ × 3³ × 7² × 13 × 7 × 13² = (2 × 3 × 7 × 13)³ ⇒a perfect cube. Therefore the smallest number is 1183 and the cube root of the product is 546.