Kareem attends chorus every 6 days and math league every 16 days. If he went to both chorus and math league today, in how many days will he participate in both activities again?

1 answer

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:

  • The prime factorization of \(6\) is: \[ 6 = 2 \times 3 \]

  • 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.