Every periodic signal repeats at all integer multiples of its period

Evidence

However, any periodic function of period T is also periodic at 2T, 3T and so on. That is, if a signal repeats itself every second, it is certainly repeating itself every two seconds. A 440 Hz sinusoid is also periodic with the same period as a 220 Hz sinusoid. Adding any two signals that are periodic with the same period gives a result with that same period. — Eric J. Heller, Why You Hear What You Hear- An…, 341