Question

the product of three consecutive numbers is 4080 what is the least number?

Answer 1

the product of three consecutive number is 4080 and the least number is 16

Answer 2

ANSWER

Let the three consecutive numbers be $x, (x+1)$ and $(x+2)$. 
Product of the three consecutive numbers = 4080

ATQ (According To Question)
Product of the three consecutive numbers = 4080
⇒ $x(x+1)(x+2)=4080$
⇒ $x(x^{2}+2x+x+2)=4080$
⇒ $x(x^{2}+3x+2)=4080$
⇒ $x^{3}+3x^{2}+2x=4080$
⇒ $x^{3}+3x^{2}+2x-4080=0$
It is very very very difficult for me to show and explain that how to factorise the polynomial on the left hand side of the equation. So, I am showing you the direct factorisation. (I'm sorry for that. )
⇒ $(x-15)(x^{2}+18x+272)=0$

Using the Zero Factor Principle: 
1) $x-15=0$
⇒ $x=15$
2) $x^{2}+18x+272=0$
⇒ $x=-9+\sqrt{191}i$, $x=-9-\sqrt{191}i$

Now, we are not referring to complex numbers, we are only referring to real numbers. So, we should only consider this solution: $x=15$

Now, 
First number = $x$ = 15
Second number = $(x+1)$ = (15 + 1) = 16
Third number = $(x+2)$ = (15 + 2) = 17

Out of these numbers, the smallest number is 15. 

∴ The least number is 15. 

Hope this may help you.