SOLUTION: Jason is filling grab bags for the school festival. Two hundred bags are lined up on a long table. He has already placed crackers and other food items in each bag and now has a l

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Question 136664: Jason is filling grab bags for the school festival. Two hundred
bags are lined up on a long table. He has already placed crackers and
other food items in each bag and now has a limited amount of prizes to
add to some of the bags. If he places prize A in every 8th bag, prize B in
every 12th bag, and prize C in every 15th bag, which bag will have all
three prizes?

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Jason is filling grab bags for the school festival. Two hundred
bags are lined up on a long table. He has already placed crackers and
other food items in each bag and now has a limited amount of prizes to
add to some of the bags. If he places prize A in every 8th bag, prize B in
every 12th bag, and prize C in every 15th bag, which bag will have all
three prizes?
----------------
You need the bag number that is divisible by 8,12,and 15.
That is the "least common multiple".
Write
8 = 2^3
12 = 2^2*3
15 = 3*5
-------------
The lcm must have each of the prime power numbers raised to its highest power.
lcm = 2^3*3^1*5^1
lcm = 8*15 = 120
----------------------
The 120th bag will have all three prizes because it is an 8th bag,
a 12th bag and a 15th bag.
================================
cheers,
Stan H.

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