Question

The LCM and HCF of two natural numbers are 480 and 12 respectively. If the numbers are in the ratio 5 : 8 and numbers are given by A and B, then find the absolute value of A - B.

Answer 1

Let the natural numbers be 5x and 8x HCF (5x, 8x) = x ;
but given HCF = $12\Rightarrow x=12$
The two numbers are
$\therefore$ 5x = 60 and 8x = 96
Alternately, LCM (5x, 8x) = 40x
$40x=480\Rightarrow x=12$
5x = 60 and 8x = 96

$A=96,B=60$

$A-B=96-60=36$