To find out when Kareem will participate in both chorus and math league again, we need to determine the least common multiple (LCM) of the two activities' frequencies: 6 days for chorus and 16 days for math league.
First, we factor each number into its prime factors:
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The prime factorization of \(6\) is: \[ 6 = 2 \times 3 \]
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The prime factorization of \(16\) is: \[ 16 = 2^4 \]
Next, to find the LCM, we take the highest power of each prime factor present in the factorizations:
- For the prime \(2\), the highest power present is \(2^4\) (from \(16\)).
- For the prime \(3\), the highest power present is \(3^1\) (from \(6\)).
Now, we can calculate the LCM by multiplying these together:
\[ \text{LCM} = 2^4 \times 3^1 = 16 \times 3 = 48 \]
Thus, the least common multiple of 6 and 16 is \(48\).
Therefore, Kareem will participate in both chorus and math league again in \( \boxed{48} \) days.
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