Bihar Police Constable Model Paper 5

Given:
It is given that A = LCM of $\left(7\mathit{x}\mathit{y}\mathit{z},5{\mathit{x}}^2{\mathit{y}}^2\mathrm{and}3{\mathit{z}}^3\right)$ and B = HCF of (xy, 3yz and -2 yzx)
Concept Used:
Basic concept of HCF and LCM
Calculation:
A = LCM of $\left(7\mathit{x}\mathit{y}\mathit{z},5{\mathit{x}}^2{\mathit{y}}^2\mathrm{and}3{\mathit{z}}^3\right)$
∴ LCM of $\left(7\mathit{x}\mathit{y}\mathit{z},5{\mathit{x}}^2{\mathit{y}}^2\mathrm{and}3{\mathit{z}}^3\right)$ = 105 ${\mathit{x}}^2{\mathit{y}}^2{\mathit{z}}^3$
Now, B = HCF of (xy, 3yz and -2 yzx)
∴ HCF of (xy, 3yz and -2 yzx) = y
Now, the value of A/B
∴ A/B = 105 ${\mathit{x}}^2{\mathit{y}}^2{\mathit{z}}^3∕\mathit{y}$ = 105 ${\mathit{x}}^2\mathit{y}{\mathit{z}}^3$
Hence, option (1) is correct