Question

I’m thinking of two numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What’s the other number I’m thinking of ?

Answer 1

$\text{lcm}(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)}\\\\\\36=\dfrac{|12b|}{6}\\\\36=\dfrac{12|b|}{6}\\\\2|b|=36\\|b|=18\\b=18 \vee b=-18$