Question

The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b

Answer 1

$\text{lcm}(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)}\\\\378=\dfrac{|a\cdot b|}{9}\\\\|a\cdot b|=42\\\\a\cdot b=-42 \vee a\cdot b=42$

So, the least value is -42