There is no solution.
3*5*7 = 105 is too small,
and the next three
5*7*9 = 315 is too large.
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Find two consecutive numbers with the value of 4160
12, 13 and 14
14, 15, 16
Let's assume the first odd number is x. Then the next two consecutive odd numbers would be x + 2 and x + 4. The product of these three numbers is x(x + 2)(x + 4) = 29667. By trial and error, we find that x = 51 satisfies this equation. Therefore, the three consecutive odd numbers are 51, 53, and 55.
15 and 13