A store manager needs to restock two items on the same schedule. Item X needs restocking every 9 days and Item Y needs restocking every 12 days. Both items were restocked today. The manager wants to know the next three dates when both items will need restocking on the same day. How many days from now will the third such date occur?
- 72 days from now
- 144 days from now
- 108 days from now (correct answer)
- 36 days from now
Explanation: When you see problems about events happening on regular schedules, you need to find the Least Common Multiple (LCM) to determine when they'll coincide.
Item X restocks every 9 days and Item Y restocks every 12 days. To find when they'll both restock together, you need the LCM of 9 and 12. Start by finding the prime factorization: and . The LCM uses the highest power of each prime factor: . This means both items will restock together every 36 days.
Since they both restocked today (day 0), the pattern will be:
The answer is C) 108 days from now.
Looking at the wrong answers: A) 72 days represents the second coincidence, not the third. B) 144 days would be the fourth coincidence (). D) 36 days is the first coincidence when both items restock together again.
The key strategy here is recognizing that "coinciding schedules" problems always require finding the LCM. Once you have that base interval, multiply it by the position number you need (first, second, third, etc.). Don't get confused by thinking the LCM itself is the final answer—it's just the repeating interval between coincidences.