Jerry plays tennis once every 6 days. Sam plays tennis every 10 days and Leo comes once every 12 days. This Monday all of them played.

60 is the HCF so they all played on the 60th day.

You need to see the HCF being 60

As on the 60th day that they played, or every 60 days that they play it becomes divisible duration of time

As; 60/6 = 10 60/10 = 6 and 60/12 = 20

This now means that when we half it or try 50,40 etc these numbers we see that 12 nor 6 is divisible on the landing number that matches 10 except for 30 but 12 doesn't divide into this and 10 doesn't divide into 48 36 or 24 etc ...