Clara is a tour guide who gives several tours over the course of a morning shift and an evening shift. Her morning shift tours are given to groups of 33 people while her evening shift tours are given to groups of 6 people. If the total number of tourists in the morning shift is the same as the total number of tourists in the evening shift, what is the minimum number of tourists that Clara guides in each shift?
Question
Clara is a tour guide who gives several tours over the course of a morning shift and an evening shift. Her morning shift tours are given to groups of 33 people while her evening shift tours are given to groups of 6 people. If the total number of tourists in the morning shift is the same as the total number of tourists in the evening shift, what is the minimum number of tourists that Clara guides in each shift?
Solution
To find the minimum number of tourists that Clara guides in each shift, we need to find the least common multiple (LCM) of the group sizes for the morning and evening shifts.
Step 1: Identify the group sizes. The morning shift group size is 33 and the evening shift group size is 6.
Step 2: Find the LCM of 33 and 6. The LCM of 33 and 6 is 198.
Therefore, the minimum number of tourists that Clara guides in each shift is 198.
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