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HCF AND LCM

Highest common factor: The highest common factor (H.C.F.) of two or more numbers is the greatest number which divides each of them exactly. It is also known as greatest common divisor (G.C.D.).
H.C.F. can be calculated by:
  1. Prime factorisation method
  2. Division method
Least common multiple: The least common multiple (L.C.M.) of two or more numbers is the smallest number which is exactly divisible by each of them.
L.C.M. can be calculated by :
  1. Prime factorisation method
  2. Division method

H.C.F. and L.C.M. of fractions

First express the given fractions in their lowest terms. Then,
 
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Formula:
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NOTE :
  • The greatest number that will exactly divide x, y, z = HCF of x, y and z.
  • The greatest number that will divide x, y and z leaving remainders a, b and c respectively = HCF of (x – a), (y – b) and (z – c ).
  • The least number which is exactly divisible by x, y and z = LCM of x, y and z.
  • The least number which when divided by x, y and z leaves the remainder a, b and c respectively=LCM of (x, y and z)–R where R = (x – a) = (y – b) = (z – c)
  • The least number which when divided by x, y and z leaves the same remainder r in each case = LCM of (x, y and z) + r
  • The greatest number that will divide x, y and z leaving the same remainder in each case = HCF of (x – y), (y – z) and (z – x).




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