Question: Show that if ( a , c ) = 1 = ( b , c ) then ( a b , c ) = 1

Show that if (a,c)=1=(b,c) then (ab,c)=1(this is Proposition 24 of
Book VII in Euclid's Elements).
Explain how to measure 8 units of water using only two jugs, one of which
holds precisely 12 units, the other holding precisely 17 units of water.

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