Final answer:
The first calculator that Ms. Shek and Ms. Velting will clean at the same time is the 144th calculator.
Step-by-step explanation:
To find the first calculator that Ms. Shek and Ms. Velting clean at the same time, we need to find the least common multiple (LCM) of 16 and 36. The LCM is the smallest number that is divisible by both 16 and 36.
The prime factorization of 16 is 2 × 2 × 2 × 2, and the prime factorization of 36 is 2 × 2 × 3 × 3.
We can see that both numbers have two 2s in their prime factorization, so we only need to take the highest power of each prime. Therefore, the LCM of 16 and 36 is 2 × 2 × 2 × 2 × 3 × 3 = 144.
Therefore, the first calculator that they will clean at the same time is the 144th calculator (option A).