TNPSC Group II · Bite-size lessons
HCF and LCM
About 6 min · Aptitude and Mental Ability · English
Time worked out from the lesson's 352 words at 150 words a minute, plus a minute for each question.
HCF (Highest Common Factor) and LCM (Lowest Common Multiple) form the backbone of number system problems in TNPSC Group II/IIA. Mastering HCF and LCM is non-negotiable because the calculations are straightforward once you understand the methods, making these reliable scoring opportunities.
Key ideas
- HCF (Highest Common Factor): The largest number that divides two or more numbers exactly without leaving a remainder. Also called GCD (Greatest Common Divisor).
- LCM (Lowest Common Multiple): The smallest number that is exactly divisible by two or more given numbers.
- Fundamental Relationship: For any two numbers a and b: HCF × LCM = a × b.
- Co-prime Numbers: Two numbers with HCF = 1 are co-prime. Their LCM equals their product directly.
- HCF of Fractions: HCF = HCF of numerators ÷ LCM of denominators
Watch out for
- Confusing HCF and LCM applications: Using LCM when HCF is needed. Fix: HCF for "greatest/largest that divides" problems; LCM for "smallest/least that is divisible" or "when will events coincide" problems.
- Applying product formula to three numbers: Writing HCF × LCM = a × b × c. Fix: The formula HCF × LCM = Product works only for exactly two numbers.
- Wrong formula for fractions: Mixing up numerator and denominator rules. Fix: Remember "HCF is smaller, so divide by larger (LCM)."
Quick reference
- HCF = Pick lowest powers of common prime factors
- LCM = Pick highest powers of all prime factors
- HCF × LCM = a × b (only for two numbers)
- "Greatest length/size that divides exactly" → Find HCF
- "Least time/number divisible by all" → Find LCM
Check yourself: 3 questions
1. Three bells toll at intervals of 9, 12, and 15 minutes respectively. If they start tolling together, after how many minutes will they toll together again?
2. The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, what is the other number?
3. Four different electronic devices beep at intervals of 6, 8, 10, and 12 seconds respectively. If they all beep together at 10:00 AM, at what time will they beep together again?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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