The circuit to light LED with single 1.5V battery is usually based on a blocking oscillator or a charge-pumped voltage doubler.
This is another (but similar to charge pump) way to flash LED with 1.5V battery. The base-R voltage becomes nearly double the Vcc while making oscillation timing of astable multivibrator. LED can be flashed if it is attached aside. Since the LED discharges the C electricity, oscillator timing is shortened.
Figure 1: 1.5V LED flasher
Normal astable multivibrator ( without LED )
LED attatched timing
LED discharged electricity
Figure 2: LTspice simulation
You can see the light at the marked points.
Figure 3: Implementation
The circuit above is not enough to light blue or white LEDs which need more than 3V voltage. This version boosts the voltage by a charge-pump extension. It produces about 2.8V momentary, with 0.8 sec intervals. Try other LEDs if the lighting is dim, since some LEDs may require the higher voltage.
Figure 4: 1.5V flasher for Blue/White LED
The V(vl) is the LED's cathode voltage, and the V(vh) is the anode.
Figure 5: LTspice simulation (blue/white)
Figure 6: Implementation (blue/white)