【Analysis】Analyze from the perspective of the parity of the sum of consecutive non-zero natural numbers: Since it is the sum of consecutive non-zero natural numbers, the sum of two numbers, odd + even = odd; the sum of three numbers, even + odd + even = odd, and it is a multiple of 3; the sum of four numbers is always even, so it is excluded; the sum of five numbers, odd + even + odd + even + odd = odd, and it is a multiple of 5; the sum of six numbers, three odd + three even = odd. The least common multiple of 3 and 5 is 15, so this smallest natural number must be a multiple of 15.

Through trial calculations, it is known that 45 is the smallest natural number that meets the conditions.
【Solution】Solution: The sum of two numbers, odd + even = odd;
The sum of three numbers, even + odd + even = odd, and it is a multiple of 3;
The sum of four numbers is always even, so it is excluded;
The sum of five numbers, odd + even + odd + even + odd = odd, and it is a multiple of 5;
The sum of six numbers, three odd + three even = odd.
The least common multiple of 3 and 5 is 15, so this smallest natural number must be a multiple of 15.
Trial calculation: \(45=22+23=14+15+16=7+8+9+10+11=5+6+7+8+9+10\)
Therefore, 45 is the smallest natural number that meets the conditions.
12. (10 points) Find the smallest natural number that can be expressed as the sum of four different sequences of at least two consecutive non-zero natural numbers.

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