RRB Group D · Bite-size lessons

LCM and HCF

About 7 min · Mathematics · English

Time worked out from the lesson's 456 words at 150 words a minute, plus a minute for each question.

LCM (Least Common Multiple) and HCF (Highest Common Factor, also called GCD — Greatest Common Divisor) form a fundamental pillar of Railway Group D Mathematics. These concepts appear not just as direct calculation problems but also disguised in word problems involving bells ringing together, meeting points of runners, grouping items, and more. Mastery of LCM and HCF is non-negotiable because they underpin questions on simplification, fractions, ratio-proportion, and time-based scenarios.

Key ideas

• HCF (Highest Common Factor) is the largest number that divides all given numbers without leaving a remainder. It represents the "biggest common piece" you can extract from the numbers. Use HCF when the problem asks for maximum size, greatest length, or largest group.
• LCM (Least Common Multiple) is the smallest number that is exactly divisible by all given numbers. It represents the first common meeting point. Use LCM when the problem asks for minimum time, shortest distance, or when events repeat together.
• Prime Factorization Method: Break each number into prime factors. For HCF, take the lowest power of common primes. For LCM, take the highest power of all primes present.
• Division Method (for HCF): Use Euclidean algorithm — repeatedly divide the larger number by the smaller, replace the larger with the remainder, until remainder is zero. The last non-zero divisor is the HCF.
• Relation between LCM and HCF: For any two numbers a and b, Product of numbers = LCM × HCF, i.e., a × b = LCM(a,b) × HCF(a,b).

Watch out for

• Mixing up LCM and HCF: Students use LCM when HCF is needed and vice versa. Fix: LCM for "together again" or "minimum"; HCF for "maximum equal parts" or "largest measure."
• Incorrectly applying fraction formulas: Writing LCM of fractions as (LCM of numerators)/(LCM of denominators). Fix: Remember — LCM fraction uses HCF in denominator; HCF fraction uses LCM in denominator. They swap.
• Forgetting to convert decimals: Attempting to find LCM of 0.6 and 0.8 directly without converting. Fix: Multiply by 10 to get 6 and 8, find LCM = 24, divide by 10 to get 2.4.

Quick reference

• LCM = smallest common multiple; use for "together again" problems.
• HCF = largest common factor; use for "maximum size/group" problems.
• Product rule (two numbers only): a × b = LCM × HCF.
• LCM of fractions = (LCM numerators)/(HCF denominators).
• HCF of fractions = (HCF numerators)/(LCM denominators).

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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