Question

Find the samllest value of K when :
280k is a perfect square
882 is a cube

Answer 1

280 = 7 x 2^3 x 5
882 = 7^2 x 2 x 3^2

For 280k to be perfect square , their powers need to be even
For 882 to be a cube, their powers need to be in multiple of 3,

To satisfy both parties,
K = 7 x 2^5 x 3^4 x 5^3 = 2268000