Problem
NT-B1-M09-P014 Smallest with \(15\) Divisors
#14
★★★☆☆ Level 3 of 5
Find the smallest positive integer with exactly \(15\) positive divisors.
\(15=15\) or \(15=5\cdot3\).
The exponent patterns are \(14\), or \(4\) and \(2\). Candidates: \(2^{14}\) and \(2^4\cdot3^2=144\). The smallest number is \(144\).
Optimisation through exponents.