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Question: An anthropologist analyzing migration patterns observes two groups moving every 14 and 21 years. What is the least common multiple of their migration intervals?
Question: A graduate student converts a base-ten number to base-six for data encoding. What is the base-ten number represented by the base-six number $2143$?
Question: An anthropologist tracks human migration events occurring every 19 and 23 years. What is the smallest number of years after which both events coincide?
Question: A pharmacologist calculates dosing intervals of 8 and 12 hours. What is the least common multiple of these intervals?
Question: A graduate student in STEM seeks the largest possible GCD of two numbers whose sum is 150. What is the maximum GCD?
Solution: The first five prime numbers are $2$, $3$, $5$, $7$, and $11$. Since these numbers are all prime, their least common multiple is simply their product:
Solution: First, observe that all the numbers are odd and consecutive odd numbers. We can reduce each number modulo $8$:
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