HCF and LCM

Understanding the Concept of HCF and LCM

  • The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides exactly into two or more numbers.
  • The Lowest Common Multiple (LCM) is the smallest positive number that is a multiple of two or more numbers.
  • For example, for the numbers 12 and 18, their HCF is 6 and their LCM is 36.

Methods for Calculating HCF and LCM

  • Listing Method:
    • List the factors or multiples of the given numbers.
    • For factors (HCF), choose the highest number which is common to all lists.
    • For multiples (LCM), choose the smallest number which is common to all lists.
  • Prime Factorisation:
    • Prime factorise the given numbers.
    • For HCF, multiply the common prime factors.
    • For LCM, multiply all prime factors, but only use common factors once.

Practice Problems

  • Problem: Find the HCF and LCM of 6 and 15 using the prime factorisation method.
    • Solution: The prime factorisation of 6 = 2 x 3. The prime factorisation of 15 = 3 x 5. The HCF is the product of common prime factors, i.e., 3. The LCM is the product of all prime factors, i.e., 2 x 3 x 5 = 30.
  • Problem: Calculate the HCF of 24 and 36 using the listing method.
    • Solution: Factors of 24 = [1,2,3,4,6,8,12,24]. Factors of 36 = [1,2,3,4,6,9,12,18,36]. The HCF (the highest common factor) is 12.

Remembering and Double Check

  • Calculating HCF and LCM correctly requires a solid understanding of multiplication, division, and factors.
  • Always double-check your calculations to ensure accuracy.
  • Different problem scenarios may require using different methods to calculate HCF or LCM. Hence it’s important to be familiar with both methods.