finding approximate 'least common factor'

[Przemek Klosowski]

I have numbers which are approximately (but not exactly) an integer 
number of some basic quantity. How would you estimate that basic 
quantum? For instance, if the data is:

a= [5500 3800 3300 3800 4000 5500 2600 3800 5500 2500 4000 6000 4000 450 
1550 1000 3800 5300 5300 1800 3800 1550 2500 3300 1300 2500 3300 2500 
1550 5500 2200 3500 3300 2200 1300 800 2200 1000 2500 5300 3000 2200 
2200 2200 4000 2400 2200 5500 4000 800 2200 2600 450 450 ]

All I could come up with is to look at all the candidates (s) and plot 
the sum of squares (d) of the integer quotient residuals (c) against the 
value of the candidates:

s=50:50:2400; for i=1:length(s);  c=a./s(i); d(i)=sumsq(c-round(c)); end
plot(s,d)

the minima on this plot show values that fit in mostly integer multiples 
into the numbers in a(), so I am eyeballing the underlying quantum to be 
650---but this is very qualitative.

Can anyone think of a more precise numerical algorithm?