Let $x, y, z$ be positive integers such that $HCF\left(x, y, z\right)=1$ and $x^2+y^2=2z^2.$ Which of the following statements are true?

$I.$ $4$ divides $x$ or $4$ divides $y$

$II.$ $3$ divides $x+y$ or $3$ divides $x-y$

$III.$ $5$ divides $z\left(x^2-y^2\right)$

Find the ratio of the LCM and the HCF of 5, 25 and 30. 

(A) 1 : 6 

(B) 30 : 1 

(C) 1 : 30 

(D) 6 : 1 

Find the HCF of 3, 7 and 15. 

(A) 7 

(B) 15 

(C) 3 

(D) 1 

What will be the HCF of $\frac{2}{3}, \frac{8}{9}$ and $\frac{64}{81}$?

The LCM of two numbers is $210$. If their HCF is $35$ and one of the numbers is $105$, find the other number:

Find the G.C.F and L.C.M of $20$and $28$.

1. $20, 280$
2. $5, 280$
3. $10, 140$
4. $4, 140$