The ratio of the sum to the LCM of two natural numbers is 7:12. If their HCF is 4, then the smaller number is :

Let the numbers be 4x and 4y where x and y are prime to each other

LCM = 4xy 

$\frac{Sum}{LCM} = \frac{7}{12}$

$\frac{x + y}{xy} = \frac{7}{12}$

$7xy−12x−12y=0$

By trial (or using factorization), if $x = 5$ and $y = 3$

Smaller number $= 4 × 3 = 12 $

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