Six bells start ringing together and ring at intervals of 4, 8, 10, 12, 15, and 20 seconds respectively. How many times will they ring together in 60 minutes?

LCM of 4, 8, 10, 12, 15 and 20 = 120
120 seconds = 2 minutes
Hence all the six bells will ring together in every 2 minutes
Hence, number of times they will ring together in 60 minutes = 1 + (60/2)
= (2+ 60)/2
= 31.

The HCF of a group of numbers will always be a factor of their LCM.
HCF is the product of all common prime factors using the least power of each common prime factor.
LCM is the product of the highest powers of all prime factors.