For every six days that Ahmad works, he gets a day off. For every seven days that Xinyi works, she gets a day off. Ahmad and Xinyi have the same day off on the 10 of March. When do they next have the same day off?
Answers
Answer:
The two people's work schedules are on 7 and 8 day cycles. Since 7 is prime, its only factors are 1 and itself. The factors of 8 are 1, 2, 4 and 8. Since the product of any of those factors × 1 results in a number not divisible by one or both original numbers, 1 can be ignored. That leaves 7, and 2, 4, and 8. 7×2=14, and 7×4=28. Neither of those results are divisible by 8. Therefore, the LCM of 7 and 8 is 7×8, or 56. So, the next common day off is 56 days away.
You stated that today was the 10th of the month, but failed to indicate which month it was. Since not all months have the same number of days, it is impossible to provide the exact date. However, 56 days is 8 weeks, as all weeks have 7 days. So, their next common day off will be 8 weeks from today.