64 (1, 2, 4, 8, 16, 32, 64)
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To find the second smallest number that has 12345 as factors, we need to consider the prime factorization of 12345, which is 3 x 5 x 823. The smallest number with 12345 as a factor is 12345 itself. The second smallest number would be obtained by multiplying 12345 by the next smallest prime number after 3 and 5, which is 7. Therefore, the second smallest number with 12345 as factors is 12345 x 7 = 86415.
Logically, the smallest number with 4 different prime factors would have to be the product of the smallest four prime numbers. So the smallest natural number with four different prime factors is 210 (2*3*5*7).
36
11
The smallest number is 504. There are no common factors other than 3x3, 2x2x2, and 7, so they must be multiplied together.