VTMO 2026 - Grade 7 - Semifinal - SET 3 - Self-study Question 21

Question 21

Positive integers $x,a,b,c$ satisfy $\dfrac x2=a^2$, $\dfrac x3=b^3$ and $\dfrac x5=c^5$. Find the smallest possible number of positive divisors of $x$.

$30$
$60$
$72$
$660$
$1232$