Question 71262: Happy Hector and Party Paul are each having a catered party at Fun Factory. Hector’s party is in the hall and Paul’s party is on the Patio. The catering manager of Fun Factory explained the rules to Hector and Paul. Both Hector’s party in the Hall and Paul’s party on the Patio must have the same size table, that is, for example, table size for 2,3,4,5,6,7,8,9, etc. The manager will only order one size table for both parties.He will order the largest size table possible. Everyone at each party must have a seat and no seats can be empty at any table. Hector will have a total of 180 people. Paul is expecting a total of 84 people. What is the largest-sized table the manager needs to order for both Hector and Paul?
Answer by sudhir(14)   (Show Source):
You can put this solution on YOUR website! This looks to me to be a problem of Greatest Common Divisor( or some say Highest Common Factor)
look at both the parties the host wants all their guests to be seated.
and the manager tells them that table size should be same for both the parties.
but he did not put any restriction on the number of tables at any of the parties.
So, now the point is to find the maximum size of the table so that the size divides exactly the number of guests at both parties .
formula for finding HCF of two numbers say 'a' and 'b' is:-
HCF = (a*b)/(LCM of a and b)
see http://en.wikipedia.org/wiki/Greatest_common_diviso
here LCM of 84 and 180 = 1260
so, size of table = 84*180/1260
= 12 Answer.
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