Electronic – Use audio frequency to light up multiple LEDs

Frequency is the inverse of time for repeating events. If a single cycle of your mains is 1/50 of a second in duration (0.02 seconds), then there will be 50 cycles in a second (1 / 0.02). We say the frequency is 50 Hz.
The unit for frequency is the Hertz (Hz). 1 Hz is equal to 1 cycle per second, an older name for it (cps). It's a convenient unit, even for very short cycles we use, with a prefix: MHz, GHz. For longer cycles (near or longer than 1 Hz) we sometimes use the minute as unit: a heart rate of 70 beats per minute (BPM), a metronome setting of 100 BPM.
Still longer cycles are often expressed as a period of time (1 / frequency).

Every system has its typical (range of) frequencies. A heartbeat will be around 1-2 Hz, and the resonance frequency of a trampoline is also in the order of 1 Hz. Radio waves have a broad range of frequencies: 30 kHz (for a corresponding wavelength of 10 km) is VLF (very low frequency), while the magnetron of a microwave oven "transmits" at 2.45 GHz. And while 30 kHz is low for radio, it's already well beyond what we acoustically can perceive.

A higher frequency (top track in the picture) of a signal will be shown on an oscilloscope as a faster repetition than a lower frequency (bottom track).

"Direct current" (DC) as a constant voltage has a frequency of 0 Hz.

Bandwidth indicates a range of frequencies, going from the lower limit to the higher. If your scope can handle signals from DC (0 Hz) up to 100 MHz, its bandwidth is 100 MHz - 0 Hz = 100 MHz.

There are two traditional exact approaches :

generate a high frequency representing the LCM of your required frequencies, and divide it to create the actual frequencies. Andy has illustrated this technique, and I suggest a modification that may make implementation easier.

The other is to divide the reference down to the GCD of your required frequencies (as they are all multiples of 100Hz and no higher frequency, 100Hz is the GCD) and multiply that.

The latter can be accomplished by generating a 100Hz signal rich in harmonics, then selecting all the required harmonics with a bank of bandpass filters. The first part of this is achieved by generating narrow spikes at a 100Hz repetition rate - the best approach to the second depends on your requirements : a "twin T" filter combined with a Q multiplier (such as a feedback loop around an opamp) can give an arbitrarily narrow passband; a traditional tuned L-C filter (or active equivalent) may be better if the reference frequency is variable across a narrow range.

A third approach is digital synthesis : sample the reference using a high frequency clock, and essentially implement one of the above approaches digitally. This is not exact; simple approaches introduce jitter of up to 1 clock period on each output ( summary: this can be mitigated with more complex calculations and a high resolution DAC).