Important HCF and LCM Formulas

  1. Factors and Multiples
    If a number 'a' divides another number 'b' exactly, we say that 'a' is a factor of 'b'. In this case, 'b' called 'a' multiples of 'a'.
  2. Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor (G.C.M)
    The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.
  3. Least Common Multiple (L.C.M.)
    The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
  4. Some Important Tricks of H.C.F. and L.C.M.
    • Product of two numbers = Their H.C.F. * Their L.C.M.
    • H.C.F. of given numbers always divides their L.C.M.
    • H.C.F. of given fractions = H.C.F. of Numerator

      L.C.M. of Denominator
    • L.C.M. of given fractions = L.C.M. of Numerator

      H.C.F. of Denominator
    • If d is the h.c.f. of two positive integers a and b, then there exist unique integer m and n, such that
      d = am + bn
    • Two numbers are said to be co-primes if their H.C.F. is 1.
    • H.C.F. of given number always divides its L.C.M