Formulas To Solve LCM & HCF Questions

Definition

HCF – Highest Common Factor (HCF) of two or more numbers is the greatest number which divides each of them exactly.

LCM – The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

 

How To Find Out LCM:

Method 1: Prime Factorization Method

  • Factorize all numbers into their prime factors
  • Make a note of all the distinct factors
  • Raise each factor to the maximum power present and multiply them all

 

How To Find Out HCF:

Method 1: Prime Factorization Method-

  • Factorize all numbers into their prime factors
  • Make a note of all the distinct factors present in all three numbers
  • Raise each factor to the minimum power present and multiply them all

Formula

  • Product of two numbers = Product of their H.C.F. and L.C.M
  • Co-primes: Two numbers are said to be co-primes if their H.C.F. is 1
  • HCM and LCM of fraction
    • HCF = HCF of Numerator/LCM of Denominators.
    • LCM = LCM of Numerator/HCF of Denominators.
    • LCM ≥ Numbers ≥ HCF
      LCM is a multiple of HCF