CAT Quant · Study & Practice

LCM

AreaNumber System DifficultyEasy–Moderate CAT weightage1–2 direct questions, plus LCM/HCF logic hidden in remainders, cyclicity and time-and-work

The Lowest Common Multiple (LCM) is the smallest positive number that every number in a given set divides into exactly. It looks like a school topic, but in CAT it quietly powers a whole family of problems — bells or lights that blink together, the smallest number that leaves the same remainder under several divisions, gear and circular-track meeting points, and the "find the next common event" set-ups that also surface in XAT and SNAP. The companion idea, HCF (the largest common divisor), pairs with LCM through one clean identity: for any two numbers, HCF × LCM = the product of the numbers. Master that relationship and you can recover a missing number from the other three quantities in seconds. This chapter builds LCM from prime factorisation, then layers on the HCF–LCM link, LCM of fractions, and the high-frequency CAT applications — bells ringing together and "least number leaving remainder r" problems of the form LCM·k + r. Throughout, the emphasis is on the fast factor-based method and the traps that cost careless candidates marks: confusing HCF with LCM, mishandling fractions, and forgetting that the identity HCF × LCM = product holds for exactly two numbers, not three or more.

Topics

1 LCM by Factorization 4 worked · 5 practice · 8-Q test Start → 2 HCF-LCM Relationship 4 worked · 5 practice · 8-Q test Start → 3 LCM Applications 4 worked · 5 practice · 8-Q test Start →

⚡ CAT shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Factorise, then take the HIGHEST power of every prime for LCM and the LOWEST power of common primes for HCF — never confuse the two.
  • For two numbers only: LCM = (a×b)/HCF and the missing number = (HCF×LCM)/known. The identity HCF×LCM = a×b breaks for three or more numbers.
  • HCF always divides LCM. If LCM/HCF is not an integer, the given pair is impossible — a quick sanity filter in tricky questions.
  • LCM of fractions = LCM(numerators)/HCF(denominators); HCF of fractions = HCF(numerators)/LCM(denominators). Reduce each fraction first.
  • Bells/lights starting together meet again after LCM(intervals); times in T seconds = T/LCM (add 1 if the starting instant is counted).
  • Least number leaving the same remainder r on division by several divisors = LCM(divisors)·k + r; if every divisor is short by a constant d, the number is LCM − d.

⚠️ Common mistakes & traps

CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Swapping the rules — taking lowest powers for LCM or highest powers for HCF.
  • Applying HCF×LCM = product of the numbers to THREE or more numbers; the identity is valid for exactly two.
  • Inverting the fraction rules — using HCF of numerators over LCM of denominators for the LCM of fractions.
  • In remainder problems, adding the remainder to each number instead of to the single LCM, or forgetting the LCM − d case when divisors fall short by a constant.
  • Counting the starting instant when the question asks "how many times after they start", which double-counts one toll/flash.

📈 CAT exam insight & PYQ analysis

LCM is rarely a standalone CAT question now; it surfaces inside Number System sets, remainder problems and time-and-work. The recurring patterns are: the HCF–LCM identity to recover a missing number, "least number leaving remainder r" (LCM·k + r) and its LCM − d variant, LCM of fractions, and "events together again" (bells, lights, circular tracks) which also appear in XAT and SNAP. Difficulty stays Easy–Moderate, but the trap-heavy remainder versions reward students who set up LCM·k + r cleanly rather than testing numbers. Prioritise the factor method and the divides-check (HCF | LCM) for speed and accuracy.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

LCM by factorisation rule?Tap to reveal
Product of each prime to its HIGHEST power
HCF by factorisation rule?Tap to reveal
Product of common primes to their LOWEST power
HCF × LCM equals (for two numbers)?Tap to reveal
The product of the two numbers (a×b)
Does HCF×LCM = product hold for three numbers?Tap to reveal
No — only for exactly two numbers
Missing number from HCF, LCM and one number?Tap to reveal
(HCF × LCM) / known number
LCM of fractions?Tap to reveal
LCM(numerators) / HCF(denominators)
HCF of fractions?Tap to reveal
HCF(numerators) / LCM(denominators)
When two bells start together, they next ring together after?Tap to reveal
LCM of the intervals
Least number leaving remainder r on several divisors?Tap to reveal
LCM(divisors) + r (general LCM·k + r)
Divisors each short of remainder by constant d — least number?Tap to reveal
LCM(divisors) − d
Quick check that HCF and LCM are consistent?Tap to reveal
HCF must divide LCM exactly
LCM of 12, 15 and 20?Tap to reveal
60

📌 Quick revision

LCM is the smallest common multiple; HCF the largest common divisor. By factorisation, LCM takes the highest power of every prime, HCF the lowest power of common primes. For two numbers, HCF × LCM = a × b, so any missing quantity is recoverable — and HCF always divides LCM. LCM of fractions = LCM(numerators)/HCF(denominators). Events that start together recur after LCM(intervals). The least number leaving remainder r on several divisors is LCM·k + r, dropping to LCM − d when each divisor falls short by a constant d. Watch the traps: don’t swap the LCM/HCF rules, don’t extend the product identity past two numbers, and don’t invert the fraction rules.

Chapter test

📝 LCM — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara CAT success checklist

You have truly mastered LCM when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (3 topics)3/3
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards