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CMAT Topics

HCF and LCM

HCF and LCM are fundamental arithmetic concepts frequently tested in TU CMAT, KUUMAT, BBA, BIM, BHM, and management entrance examinations. They form the basis for solving problems involving divisibility, fractions, ratios, time cycles, and number theory.

Practice MCQs for HCF and LCM

Fundamental Principles

Factor

A factor of a number is an exact divisor of that number.

Multiple

A multiple of a number is obtained by multiplying it by integers.

Highest Common Factor (HCF)

The largest number that divides two or more numbers exactly.

Greatest Common Divisor (GCD)

Another name for HCF.

Least Common Multiple (LCM)

The smallest positive number that is divisible by each of the given numbers.

Prime Factorization

Expressing a number as a product of prime numbers.

Co-prime Numbers

Two numbers whose HCF is 1.

Essential Formulation Tips

  • Use prime factorization for large numbers.
  • Use Euclidean division method for quick HCF calculations.
  • Always check if numbers are co-prime first.
  • For repeating events, think LCM.
  • For equal grouping or division, think HCF.

Shortcut Execution Techniques

  • If two numbers are co-prime, their LCM is simply their product.
  • HCF of consecutive integers is always 1.
  • LCM of consecutive co-prime integers equals their product.
  • To find HCF quickly, repeatedly divide larger number by smaller number.
  • LCM problems often appear in clock, bell, and work cycle questions.

Contextual Inquiries (FAQs)

Q: What is the difference between HCF and LCM?

A: HCF is the largest common factor, whereas LCM is the smallest common multiple.

Q: When should I use HCF in word problems?

A: Use HCF when dividing objects into the largest equal groups.

Q: When should I use LCM in word problems?

A: Use LCM when finding when repeating events occur together.