LCM and HCF Question Types, Concepts, Strategies, Short Tricks

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Published on 3 August 2026 by

Key Takeaways

  • LCM and HCF questions are crucial for competitive exams like SSC, Banking, and RRB, as they assess problem-solving skills in various scenarios.
  • Understanding LCM (Least Common Multiple) and HCF (Highest Common Factor) helps candidates tackle divisibility, fractions, and time-based problems effectively.
  • Candidates encounter different types of LCM and HCF questions: direct, word-based, application, and mixed concept problems.
  • Key formulas, such as HCF × LCM = Product of Numbers, aid in quickly solving LCM and HCF questions during exams.
  • Employ tricks like prime factorization and the product rule to enhance speed and accuracy when solving LCM and HCF questions.

LCM (Least Common Multiple) and HCF (Highest Common Factor) form the backbone of many Quantitative Aptitude questions in SSC, Banking, and RRB exams. This topic is tested directly as well as indirectly in problems related to time, work, trains, pipes, and ratios. In this blog, we have provided all the details including definitions of LCM and HCF, short notes, formulas, tricks, solved questions, and more.

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What is LCM and HCF for Bank Exams and other Exams?

LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers, while HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. These concepts are commonly used in competitive exams for solving questions related to divisibility, fractions, time-based situations and word problems. To solve LCM and HCF questions efficiently, candidates should understand factorisation methods, prime numbers, divisibility rules and logical elimination techniques.

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Why is LCM and HCF important in competitive exams?

In almost every competitive exam, at least one question is asked from LCM and HCF. Since the topic is concept-based, candidates who revise formulas and tricks can solve these questions in under 30 seconds.

ExamNo. of QuestionsDifficulty
SSC CGL / SSC CHSL1-2Easy
IBPS PO / SBI PO 1-2Moderate
RRB NTPC / RRB Group D1Easy
State PSC / Police1–2Moderate

LCM and HCF Quantitative Aptitude Short Notes

Before solving exam questions, revise these quick points:

TermMeaningExample
LCMSmallest multiple of given numbersLCM of 4, 6 = 12
HCFGreatest divisor of given numbersHCF of 12, 18 = 6
Product RuleHCF × LCM = Product of Numbers (for two numbers)For 12, 18 → HCF=6, LCM=36 → 6×36=12×18
Prime FactorizationMethod of finding HCF & LCM using prime numbers12=2²×3, 18=2×3²
Division MethodStep-wise division to find HCFApplied to 42 and 56 → HCF=14
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What are the Types of LCM and HCF Questions in Quantitative Aptitude?

In competitive exams, questions are framed in different ways:

  • Direct Questions – Find LCM/HCF of two or more numbers.
  • Word Problems – Based on time, work, and periodic events.
  • Application-Based – Problems involving pipes, trains, or bells ringing.
  • Mixed Concept – Combined with ratio, percentages, or algebra.
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LCM and HCF Formulas for Quantitative Aptitude

The formulas to calculate the LCM and HCF of a given set of numbers are as follows:

  • HCF × LCM = Product of Numbers (for 2 numbers)
  • HCF of fractions = HCF of numerators ÷ LCM of denominators
  • LCM of fractions = LCM of numerators ÷ HCF of denominators
  • If two numbers are coprime – HCF = 1, LCM = Product of numbers
  • LCM (a, b, c) = Smallest number divisible by all three

LCM and HCF Tricks for SSC CGL and Other Exams

Tricks to solve questions based on LCM and HCF are as follows:

  1. Always start with prime factorization for speed.
  2. Use the product rule to check accuracy.
  3. For word problems, identify if it is asking meeting time (LCM) or division problem (HCF).
  4. Eliminate options using divisibility rules.
  5. For large numbers, use the division method instead of factorization.
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FAQs

Q1. How to solve LCM and HCF questions fast?

Use prime factorization or product rule.

Q2. What is the formula for LCM of fractions?

LCM = LCM of numerators ÷ HCF of denominators.

Q3. What is the formula for HCF of fractions?

HCF = HCF of numerators ÷ LCM of denominators.

Q4. What is co-prime in LCM-HCF?

Numbers with HCF = 1.

Q5. How many types of questions are asked in LCM-HCF?

Direct, word-based, application, and mixed concept.