Question

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12, minutes respectively. How many times do they toll together in 30 hours?

Answer 1

Six bells toll together at intervals of 2, 4, 6, 8, 10 and 12 minutes, respectively.
Prime factorisation:
$$\begin{gathered} 2=2 \\ 4=2\times 2 \\ 6=2\times 3 \\ 8=2\times 2\times 2 \\ 10=2\times 5 \\ 12=2\times 2\times 3 \end{gathered}$$

∴ ​$LCM(2,4,6,8,10,12)$ = $2^3\times 3\times 5=120$
Hence, after every 120 minutes (i.e. 2 hours), they will toll together.
∴ Required number of times = $(\frac{30}{2}+1)=16$