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A supplier receives orders from 5 different buyers. Each buyer places their order only on a Monday. The first buyer places the order after every 2 weeks, the second buyer, after every 6 weeks, the third buyer, after every 8 weeks, the fourth buyer, every 4 weeks, and the fifth buyer, after every 3 weeks. It is known that on January 1st, which was a Monday, each of these five buyers placed an order with the supplier.
On how many occasions, in the same year, will these buyers place their orders together excluding the order placed on January 1st?
The supplier receives his orders from the five buyers once every 2 weeks, once every 6 weeks, once every 8 weeks, once every 4 weeks, and once every 3 weeks.
The number of occasions where all the five buyers place the order on the same day is :
The LCM of the 5-time frames during which the 5 buyers place their orders :
Hence the LCM is :
(2, 6, 8, 4, 3).
= 24 weeks.
Once every 24 weeks, all five of them place the order simultaneously.
A year has 53 weeks in total :
Hence all five of them place the orders after 24 weeks, 48 weeks.
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