10=2×5, 12=2×2×3, 15=3×5.
The smallest number they will all divide into must be 2×2×3×5=60.
So after 60 minutes one bell tolls for the 6th time, the second bell tolls for the 5th time, and the third bell tolls for the 4th time, all tolling at the same time. They toll together every hour. So the next time they toll at the same time is 1pm.