SOLUTION: Tim is buying packages of paper plates and cups. He wants to have equal amounts of each, but plates come 24 per pack, and cups come 16 per pack. What is the least amount of plates

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Question 616957: Tim is buying packages of paper plates and cups. He wants to have equal amounts of each, but plates come 24 per pack, and cups come 16 per pack. What is the least amount of plates and cups Tim will have to buy to get the same number of each?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
48. Which is 2 packs of plates and 3 packs of cups.
So what is that math behind that?
Find the prime factorization for each (24 and 16)
24 = 2*2*2*3
16 = 2*2*2*2
Now pick the factor from each that occur the most
there are 3 factors of 2 in 24; and 4 factors of 2 in 16. So use 4 factors of 2
24 has one factor of 3; 16 has none.l so use one factor of 3.
That is all the prime factors 24 and 16 have in them.
Now multiple the largest occurrences together
2%2A2%2A2%2A2+%2A+3=+48
for this case, the answer was simple enough to see without doing all the math. But you need to know the math for the harder problems ahead.