How many low-power batteries to power up 12V LEDs?
Y'all feel free to tidy.
I may come back to it.
Content should be OK.
Rushing.

If they are White LEDs Vled ~= 3.2V -3.5V typically.
3 are placed in series with a resistor so VLEds = 9.6V - 10.5V typically.
VLED varies with current and batch and device.
Balance of voltage is dropped across Rser = series R.
If they spec at say 13V and if say Vled avg = 3.3V then VLEDS = 9.9V
so Vr = (13-9.9) = 3.1V.
Nominal rated current flows when Vr = 3.1V.
So I_wrt_nominal ~~~~~= (Vin-9.9V)/3.1 x Irated.
So at say 15V I = (15-9.9)/3.1 Irated
= 5.1/3 Ir ~= 1.6 x Irated.   

As I rises VLED also rises so actual I will be lower than shown.
eg If VLED rises to 3.5V then VLEDS
= 10.5V and
I = (15-10.5)/3.1 = 4.5/3.1 x Ir ~= 1.45 x Irated. 

And at say Vin = 11V
I = (11-9.9)/3.1 x Irated
= 1.1/3.1 x Ir ~= 0.35 x I rated. 

Again, VLED changes as I changes so here Vled may be say 3V so Vleds = 9V so I is now
(11-9)/3.1 Ir = 2/3.1 Ir = 0.65 Irated. 

SO IF strip is rated at say 13V as above current MAY be about 2/3 rated value at 11V in and ABOUT 50% above Irated at 15V in. 

For a modern phosphor LED 150% is too high - about 120% is typical allowed abs max.
A responsible manufacturer will arrange current so about 120% of rated current flows when Vin is at abs max value liable to be experienced.   

A typical manufacturer won't.
Alas.   

Manufacturers of lower end products know that buyers equate bright with good and push I up. 

If you care you can add a constant current source.
An LM317 does this well but needs 2V+ drop to operate.
The two transistor cct that is often suggested is usually "not nice" but here may be OK.   Vdrop min is probably around 1V so it makes the brightness noticeably lower at Vin low but saves your LEDs at Vin high.   

For max range at constant current a cheap transistor (bipolar or FET) + an opamp section can do well.
An eg LM324 gives 4 x opamps in a cheap pkg (&lt; $1 in 1 in US retail, about 5c in volume in Asia).
If interested ask about opamp and constant current circuits.