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GATE Overflow | Mathematics | Test 1 | Question: 17

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The set $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM and GCD represents which of the following algebraic structure?

  1. group  
  2. ring 
  3. lattice 
  4. field  
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1 Answer

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If you construct a Hasse Diagram for the given set with the relation x divides y,

you will find that LCM of two numbers will be the least upper bound of those two elements and GCD will be the greatest lower bound of the elements and for every two elements we have Infimum and Supremum.

This is nothing but definition of a Lattice.

Hence option C.
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