### Find the Pythagorean triplet whose smallet member is $12.$

$(12,35,37)$

Step by Step Explanation:
1. For every natural number $m > 1$, $(2m,m^2-1,m^2 +1)$ is a Pythagorean triplet.
Putting $2m = 12$, we get $m = 6.$

Thus,
$m^2-1 = 6^2 - 1 = 35$
$m^2+1 = 6^2 + 1 = 37$
2. Hence, $(12,35,37)$ is a Pythagorean triplet.