HCF and LCM

Definition of HCF and LCM

  • The Highest Common Factor (HCF) and Least Common Multiple (LCM) are two fundamental concepts in number theory.
  • HCF is the largest number that divides exactly into two or more numbers. It is essentially the ‘greatest common divisor’.
  • LCM, on the other hand, is the smallest number that two or more numbers divide into exactly.

Finding the HCF and LCM

Prime Factorisation Method

  • The HCF is obtained by multiplying the common prime factors of the given numbers.
  • The LCM is calculated by multiplying the highest powers of all primes in the given numbers.

Division Method

  • For the HCF, the division method involves dividing the larger number by the smaller number and then dividing the divisor by the remainder until zero is obtained.
  • For LCM, the division method involves division by prime numbers until the value of the number is reduced to 1.

Applications of HCF and LCM

  • HCF and LCM have various applications, including problem-solving in areaslike number theory, abstract algebra and number systems.
  • They can be used to simplify fractions, find the least common denumerator and so on.

Common Mistakes with HCF and LCM

  • Not including every factor when calculating the LCM is a common mistake. Make sure to include all the factors of the given numbers, including those that appear multiple times.
  • Misunderstanding the definition of HCF and LCM - the HCF should be the largest factor common to both numbers, while the LCM should be the smallest multiple of them.
  • Confusing the methods for finding the HCF and LCM. Each concept has distinct methods for calculation. It’s important to ensure that the right method is used for the right concept.