Candy boxes

You are supposed to create as many identical boxes of chocolates as possible from a total of 280 nut, 252 nougat and 420 marzipan candies. You must not leave any candy behind or missing any. What will be the composition of one box and how many can you make from the given amount of candies?

Final Answer:

a =  10
b =  9
c =  15

Step-by-step explanation:

$$\begin{gathered} 280=2^3\cdot 5\cdot 7 \\ 252=2^2\cdot 3^2\cdot 7 \\ 420=2^2\cdot 3\cdot 5\cdot 7 \\ \text{GCD}(280,252,420)=2^2\cdot 7=28 \\ D=GCD(280,252,420)=28 \\ a=280/D=280/28=10 \end{gathered}$$

$b=252/D=252/28=9$

$c=420/D=420/28=15$

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