Gary performed the following three operations: 15 ÷ x, 21 ÷ x and 6 ÷ x. If he never got a remainder and x is an integer greater than 1, what is the value of x?
From these assumptions follows:
$\displaystyle ax = 15$
$\displaystyle bx = 21$
$\displaystyle cx = 6$
Where $\displaystyle x> 1, a,b,c$ are natural numbers.
Now we can write out the possible values of $\displaystyle x$
$\displaystyle x|6$ gives possible values $\displaystyle x= 2,3,6$
$\displaystyle x|21$ gives possible values $\displaystyle x = 3,7,21$
$\displaystyle x|15$ gives possible values $\displaystyle x = 3,5,15 $
What is the only possible number $\displaystyle x$ in all 3 lists?