Let [tex]p[/tex] and [tex]q[/tex] be two numbers, such that
[tex]10000 < 210p < 11000, \quad 10000 < 210q < 11000[/tex]
If [tex]p[/tex] and [tex]q[/tex] have no common factors, the greatest common factor between [tex]210p[/tex] and [tex]210 q[/tex] is obviously 210.
If we divide the inequalities above by 210, we see that
[tex]\dfrac{10000}{210} < p < \dfrac{11000}{210}, \quad \dfrac{10000}{210}< q< \dfrac{11000}{210}[/tex]
And rounding to the nearest integer, we deduce that [tex]p[/tex] and [tex]q[/tex] must be between 48 and 52.
We may pick [tex]p=49[/tex] and [tex]q=50[/tex], because they have no common factors. So, our numbers would be
[tex]210\cdot 49=10290,\quad 210\cdot 50=10500[/tex]
