Answer:
180
Explanation:
You want the smallest positive integer with 6 odd divisors and 12 even divisors among the positive integers.
Divisors
Where 'a' and 'b' are distinct primes the number of divisors of (a^m)(b^n) is (m+1)(n+1).
Application
We can solve this problem by finding an odd integer with 6 divisors. Recognizing that 6 = 6·1 = 3·2, we know that 6 odd divisors will be had by 3⁵ = 243, or by 3²·5 = 45.
We can multiply the smallest of these (45) by 2² to get a number with (2+1)(6) = 18 divisors.
4·45 = 180 has divisors ...
1, 2, 3, 4, 5, 6, 9, 10, 12,
15, 18, 20, 30, 36, 45, 60, 90, 180 . . . . . odd divisors are highlighted
The smallest positive integer with 6 odd and 12 even divisors is 180.