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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【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.