HCF and LCM Questions and Answers (Aptitude Test)
HCF (Highest Common Factor) and LCM (Least Common Multiple) are important topics in aptitude examinations, Loksewa, banking exams, SSC, railway exams, engineering entrance tests, and placement assessments. These concepts help solve problems involving divisibility, fractions, cycles, and number relationships.
In this section, you will learn HCF and LCM fundamentals, divisibility concepts, shortcut methods, solved examples, and practice questions covering factorization, fractions, word problems, and advanced applications.
Practice Sets
HCF Basics
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LCM Basics
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Divisibility Applications
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Fraction Problems
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Word Problems
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Number Applications
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Advanced HCF-LCM
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Mixed Practice
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Important HCF and LCM Concepts
Quick Tricks for HCF and LCM
Solve HCF and LCM questions faster using these techniques:
- →Use prime factorization for large numbers
- →HCF is obtained by taking common factors with smallest powers
- →LCM is obtained by taking all factors with highest powers
- →For two numbers: HCF × LCM = Product of the numbers
- →Use Euclid's division method for finding HCF quickly
- →Convert fraction simplification problems into HCF questions
- →Repeated event problems are usually solved using LCM
- →Check divisibility before performing lengthy calculations
- →Practice factor trees to improve speed and accuracy
Frequently Asked Questions
What is HCF?
HCF (Highest Common Factor) is the greatest number that divides two or more numbers exactly without leaving a remainder.
What is LCM?
LCM (Least Common Multiple) is the smallest positive number that is divisible by two or more given numbers.
What is the relationship between HCF and LCM?
For two numbers, HCF × LCM equals the product of the numbers.
Which method is best for finding HCF and LCM?
Prime factorization is the most commonly used and reliable method, while Euclid's algorithm is efficient for large numbers.
Where is LCM used in aptitude exams?
LCM is frequently used in problems involving repeated events, schedules, cycles, and synchronization questions.
Why are HCF and LCM important in aptitude exams?
They form the foundation of number theory and are commonly tested in divisibility, fraction, ratio, and word-based mathematical problems.
Related Topics
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