LCM and HCF
About 6 min · Mathematics · English
Time worked out from the lesson's 317 words at 150 words a minute, plus a minute for each question.
LCM (Least Common Multiple) and HCF (Highest Common Factor, also called GCD) form the foundation for solving numerous problems in RRB NTPC Mathematics.
Key ideas
- HCF (Highest Common Factor) is the largest number that divides all given numbers exactly. Think of it as the greatest measure that fits into each quantity without remainder.
- LCM (Least Common Multiple) is the smallest number that is a multiple of all given numbers. It represents the first point where all cycles align or the smallest quantity divisible by each number.
- Prime factorization method: Express each number as a product of primes. HCF = product of common prime factors with lowest powers; LCM = product of all prime factors with highest powers.
- Division method (for HCF): Repeatedly divide the larger number by the smaller and replace the larger with the remainder until remainder is zero. The last divisor is the HCF. Also called Euclidean algorithm.
- Relationship formula: For any two numbers a and b, LCM(a, b) × HCF(a, b) = a × b. This shortcut is gold for RRB NTPC MCQs when three of the four values are known.
Quick reference
- LCM × HCF = a × b (two numbers only) — fast shortcut for MCQs.
- HCF of fractions = (HCF of tops) / (LCM of bottoms)
- LCM of fractions = (LCM of tops) / (HCF of bottoms)
- Word problem clues: "together again/simultaneously/least" → LCM; "maximum equal parts/greatest measure" → HCF.
- Decimals: Make equal decimal places → compute as integers → restore decimal point.
Check yourself: 3 questions
1. Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time 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, find the other number.
3. Find the HCF of 0.54, 1.8 and 7.2.
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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