LCM and HCF Practice Test 4

Let the numbers be x and y which is the largest and smallest respectively.
LCM of two positive integers = 2x
Difference between small number and GCD of two numbers is 4.
y - GCD = 4
y - 4 = GCD
We know that
Product of two numbers = Product of GCD × LCM
$\mathit{x}\times \mathit{y}=\left(\mathit{y}-4\right)2\mathit{x}$
$\mathit{x}\mathit{y}=2\mathit{x}\mathit{y}-8\mathit{x}$
$2\mathit{x}\mathit{y}-\mathit{x}\mathit{y}=8\mathit{x}$
$\mathit{x}\mathit{y}=8\mathit{x}$
$\mathit{y}=8$So, the smallest number $\mathit{y}=8$