MHB What Is the Minimum Number of Meeting Times Needed for Overlapping Committees?

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The computer science department has 6 committees that meet once a month. How many different meeting times (in a month) must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are given below.

C1 = {Daim, Viknesh, Lila}, C2 = {Viknesh, Johanes, Philo}, C3 = {Daim, Lila, Philo},
C4 = {Johanes, Lila, Philo}, C5 = {Daim, Lila}, C6 = {Viknesh, Daim, Philo}
 
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