Two numbers have HCF 12 and LCM 360. What is the smallest possible value of their sum?

Write them as $12a$ and $12b$ with a, $b$ co-prime and $ab=360÷12=30$. Co-prime pairs: (1, 30), (2, 15), (3, 10), (5, 6), with sums 31, 17, 13, 11. Least sum = $12\times 11=132$ (the numbers 60 and 72).