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If $a\times b=2$, $b\times c=24$, $c\times a=3$ and $a$, $b$ and $c$ are all positive, what is the value of $a+b+c$?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.