Calendar Conundrum

Team: 
Ninja Sharks
Topic: Sequences, Series & Patterns
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Judith received a gift on the first day of the year and every sixth day after that. Mort received a gift on the fourth day of the year and every fifth day after that. Kale received a gift on the ninth day of the year and every fourth day after that. On how many days during the year did all three receive a gift on the same day?

Common Core Standards: 6.NS.4
Problem #: 
210 (2011-2012)
Problem Difficulty Level: 5 [?]