The gcd(a, b) = 9, the lcm(a, b)=378. find the least possible value of a+b.

which means there is some integer for which .

Because and , there are integers such that and , and



We have , which means there are four possible choices of :

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for :

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of is 117.

Where are the functions?