LCM and HCF Practice Test 2

HCF = 23. Let the numbers be 23x and 23y
LCM $=\frac{\mathrm{Product}\mathrm{of}\mathrm{numbers}}{\mathrm{HCF}}$
LCM $=\frac{22,218}{23}$
LCM = 966 LCM $=23\times \mathit{x}\times \mathit{y}$
$966=23\times \mathit{x}\times \mathit{y}$
$\mathit{x}\times \mathit{y}=42$
So, the possible pairs are (1, 42), (3, 14) and (6, 7)
Alternative method
HCF = 23
So let the numbers = 23x and 23y
Product of numbers = 22,218
$23\mathit{x}\times 23\mathit{y}=22,218$
$\mathit{x}\times \mathit{y}=\frac{22,218}{23\times 23}$
$\mathit{x}\times \mathit{y}=42$
So, possible pairs are (1, 42), (3, 14) and (6, 7)