The product of three consecutive numbers is 120 . Find the numbers. A \( 1 ; 2 ; 3 \) B \( \quad 2 ; 3 ; 4 \) C \( \quad 3 ; 4 ; 5 \) D \( \quad 4 ; 5 ; 6 \)

To find three consecutive numbers whose product is 120, let's denote the numbers as \( x, x+1, x+2 \). The equation becomes \( x(x + 1)(x + 2) = 120 \). Solving this will help us find the correct set of numbers. When you test the options, you'll discover that \( 4 \times 5 \times 6 = 120 \), so the correct answer is \( D \) \( 4 ; 5 ; 6 \). Speaking of consecutive numbers, did you know that the product of three consecutive numbers can give you fascinating insights into combinations? You can find interesting patterns in multiplication that reflect how number sequences work, revealing links to more complex mathematical concepts like factorials and permutations. If you're ever stuck on a problem like this, a common mistake is forgetting to check whether the numbers fall within the range of options provided. When analyzing products, it can be helpful to calculate and compare by simplifying step-by-step or even making a quick guess based on nearby multiples, ensuring you’re not missing a potential solution.