LCM and HCF

About 6 min · Quantitative Ability · English

Time worked out from the lesson's 372 words at 150 words a minute, plus a minute for each question.

LCM (Lowest Common Multiple) and HCF (Highest Common Factor) form a foundational topic in Quantitative Ability for HSSC CET. Questions from this topic appear either as direct calculation problems or as applications in word problems involving time, work, and measurement scenarios.

Key ideas

HCF (Highest Common Factor): The largest number that divides two or more numbers exactly. Also called GCD (Greatest Common Divisor). Example: HCF of 12 and 18 is 6.
LCM (Lowest Common Multiple): The smallest number that is exactly divisible by two or more numbers. Example: LCM of 4 and 6 is 12.
Relationship between LCM and HCF: For any two numbers a and b, LCM × HCF = a × b. This formula is crucial for solving problems where one value is missing.
Co-prime numbers: Two numbers with HCF = 1. Example: 8 and 15 are co-prime. For co-primes, LCM = product of the numbers.
LCM is always ≥ the largest number: LCM of any set of numbers is at least as large as the biggest number in that set.

Watch out for

Confusing LCM and HCF: Students sometimes calculate LCM when HCF is asked and vice versa. → Remember: "divide" problems need HCF; "meeting again" or "together" problems need LCM.
Using LCM × HCF formula for more than two numbers: The product formula works only for two numbers. → For three or more numbers, use prime factorization directly.
Wrong power selection in prime factorization: Taking highest power for HCF or lowest power for LCM. → HCF needs LOWEST powers; LCM needs HIGHEST powers.

Quick reference

HCF = largest common divisor; LCM = smallest common multiple
Two numbers: LCM × HCF = Product of the numbers
HCF: pick LOWEST powers; LCM: pick HIGHEST powers
"Largest number dividing..." = Find HCF (subtract remainders first)
"Ring together again / meet again" = Find LCM

Check yourself: 3 questions

1. Find the HCF of 24 and 36.
2. The LCM of two numbers is 180 and their HCF is 6. If one number is 30, find the other number.
3. Three bells ring at intervals of 12 minutes, 15 minutes and 18 minutes respectively. If they all ring together at 9:00 AM, at what time will they next ring together?

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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