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Friday 9 August 2013

L.C.M. & H.C.F.

  • PRODUCT OF TWO NUMBERS = H.C.F OF THE NUMBERS * L.C.M OF THE NUMBERS
  • TE GREATEST NUMBERS WHICH DIVIDE THE NUMBER x,y,z LEAVING REMAINDERS a,b,c, RESPECTIVELY. 
H.C.F OF ( x-a) , (y-b), (z-c) 
( THIS IS TRUE FOR ANY NUMBER.)
  • THE LEAST NUMBER WHICH WHEN DIVIDED BY x,y,z LEAVES THE REMAINDER a,b,c RESPECTIVELY IS GIVEN BY { L.C.M OF (x,y,z) } - k WHERE K= (x-a)= (y-b)= (z-c).
THIS IS TRUE FOR ANY NUMBER.
  • THE LEAST NUMBER WHICH WHEN DIVIDED BY x,y,z AND LEAVES THE SAME REMAINDER K IN EACH CASE IS GIVEN BY { L.C.M. OF (x,y,z)+ k}.



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