Ann,Julie and ,Dora are planning a series of events for their community center ann want to host an even every 12 days Julie every 15 days and Dora every 18 days They want to schedule the events such that all three events happen on the same day What is the smallest number of days?
Answer (1)
To find the smallest number of days when all three events (Ann's, Julie's, and Dora's) will occur on the same day, we need to find the least common multiple (LCM) of 12, 15, and 18.Here's how to calculate the LCM:1. Prime Factorization: - 12 = 2 × 2 × 3 - 15 = 3 × 5 - 18 = 2 × 3 × 32. Find the highest powers of all prime factors: - 2: The highest power is \(2^2\) (from 12). - 3: The highest power is \(3^2\) (from 18). - 5: The highest power is \(5^1\) (from 15).3. Multiply the highest powers: - LCM = \(2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180\).So, the smallest number of days when all three events will happen on the same day is 180 days.
