Three bells toll at different intervals. Bell A tolls every 24 seconds, Bell B tolls every 60 seconds and Bell C tolls every 90 seconds. The three bells toll together at 1100 hrs.

a) find the number of times all three bells toll together between 1100 and 1200 hours.

b) find the number of times only two bells toll together between 1100 and 1200 hours.

I am able to solve (b) by finding the Lowest Common Multiple. But I can't solve (b) short of making of list of the times each bell tolls. My answer is 30. But, there must be a shorter way to solve this. Can somebody please help?