HCF and LCM
About 6 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 325 words at 150 words a minute, plus a minute for each question.
These questions test both direct calculation skills and problem-solving through word problems involving time intervals, bell ringing, meeting points, and gear rotations.
Key ideas
- HCF (Highest Common Factor): The largest number that divides all given numbers without remainder. Used when we need the greatest common measure, largest size of identical groups, or maximum capacity that divides quantities evenly.
- LCM (Lowest Common Multiple): The smallest number that is a multiple of all given numbers. Applied when we need the smallest common interval, first simultaneous occurrence, or minimum quantity divisible by all given numbers.
- Prime Factorization Method: Express each number as a product of prime factors. For HCF, take the product of common prime factors with lowest powers. For LCM, take the product of all prime factors with highest powers.
- Division Method for HCF: Divide the larger number by the smaller, then divide the previous divisor by the remainder. Continue until remainder is zero; the last divisor is the HCF. This is the Euclidean algorithm.
- Division Method for LCM: Arrange numbers in a row, divide by common prime factors, bring down undivided numbers. Continue until no common factors remain. LCM = product of all divisors and remaining numbers.
Quick reference
- HCF × LCM = Product (for exactly two numbers only)
- HCF formula for fractions: (HCF numerators)/(LCM denominators)
- LCM formula for fractions: (LCM numerators)/(HCF denominators)
- Word problem clue: "Greatest/maximum that divides" → HCF
- Word problem clue: "Least/smallest common" or "together again" → LCM
Check yourself: 3 questions
1. The LCM of two numbers is 180 and their HCF is 12. If one of the numbers is 36, what is the other number?
2. Three bells ring at intervals of 9, 12 and 15 minutes respectively. If they all ring together at 8:00 AM, at what time will they ring together again?
3. The HCF of two numbers is 15 and their LCM is 300. If one number is 60, find the other number.
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.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.