Problem
NT-B1-M09-P022 Odd Number with \(12\) Divisors
#22
★★★★☆ Level 4 of 5
Find the smallest odd positive integer with exactly \(12\) positive divisors.
Use primes \(3,5,7,\ldots\) instead of \(2,3,5,\ldots\).
For \(12\) divisors, the exponent patterns are as before. Odd candidates include \(3^{11}\), \(3^5\cdot5\), \(3^3\cdot5^2\), \(3^2\cdot5\cdot7=315\). The smallest is \(315\). Answer: \(315\).
Adds the condition “odd”.