Question

find the smallest integer n so that 5×12×n is the product of three consecutive integers

Answer 1

This type of questions , you can solve by Hit and trail method' .
given , 5 × 12 × n = 60n
question said " smallest integer value of n so that 60n is the product of three consecutive integers.

Let n = 1 then, 60 × 1 = 60
Let's try to break it ,
60 = 2 × 2 × 3 × 5 = 3 × 4 × 5
What you see, 60 is the product of three consecutive integers 3, 4, 5

Hence, smallest integer value of n is 1.

Answer 2

Hi ,

5 × 12 × n = 60n 

If n = 1 ,

5 × 12 × 1 = 60

                 = 3 × 4 × 5 ( product of consecutive integers )

required smallest integer n = 1 

I hope this helps you .

: )