Two bells chiming five and four times a minute

Two bells start chiming at the same instant. One chimes $5$ times per minute and the other $4$ times per minute, each at evenly spaced intervals. After how long do they next chime at the same moment?

After 1 minute. The gaps are $12$ and $15$ seconds, and the first common multiple is $\operatorname{lcm}(12,15)=60$ seconds. (If "5 times a minute" counts both ends of the minute, the gaps are $15$ and $20$ seconds, and the answer is still $60$ seconds.)