Euclid's quick HCF

You will write Euclid's division method as a function, build the LCM from it, and use both on a timetable.

The idea. While $b$ is not $0$, replace the pair $(a, b)$ by $(b, r)$, where $r$ is the remainder of $a$ divided by $b$. When $b$ reaches $0$, the HCF is $a$. Then LCM $= \dfrac{a \times b}{\text{HCF}}$.

Your tasks.

1. In hcf, write Euclid's method and return the HCF.
2. In lcm, return the LCM of two numbers, using hcf.
3. Three ferries leave a jetty together. They return every $36$, $48$ and $60$ minutes. Set together to the minutes until all three are back together for the first time.