240 has 20 factors.
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The smallest number that is divisible by 20 and 15 is 60.
72 is the second-smallest number with 12 factors. Its divisors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The smallest number with 12 factors is 60. Its divisors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
16 has five factors.
180, with factors 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90 and 180.