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Aptitude Topics

HCF & LCM

HCF and LCM are fundamental concepts in number systems that help solve problems related to factors, multiples, fractions, and real-life scenarios like grouping and scheduling.

Fundamental Principles

Highest Common Factor (HCF)

The greatest number that divides two or more numbers exactly without leaving a remainder.

Least Common Multiple (LCM)

The smallest number that is a multiple of two or more numbers.

Essential Formulation Tips

  • Use prime factorization for accurate HCF and LCM.
  • HCF is always less than or equal to the smallest number.
  • LCM is always greater than or equal to the largest number.
  • For two numbers: HCF × LCM = Product of numbers.

Shortcut Execution Techniques

  • HCF of two numbers → Find common prime factors and multiply them.
  • LCM of two numbers → Multiply highest powers of all prime factors.
  • For co-prime numbers → HCF = 1 and LCM = product of numbers.
  • Use division method for faster calculations in exams.

Contextual Inquiries (FAQs)

Q: What is the difference between HCF and LCM?

A: HCF finds the greatest common divisor, while LCM finds the smallest common multiple.

Q: Can HCF be greater than LCM?

A: No, HCF is always less than or equal to LCM.

Q: When do we use LCM in real life?

A: LCM is used in scheduling problems, like finding when events will occur together.