Eduqo
Quantitative Aptitude›Ch 1: Arithmetic Foundations›HCF and LCM
Master prime factorisation, formulas, and time-interval word problems quickly.
For any two positive integers, the product of the numbers always equals the product of their HCF and LCM. This core property lets you easily find an unknown number if one number, HCF, and LCM are given.
Memory Hooks
| Concept | Best Method | Key Clue in Question |
|---|---|---|
| HCF of large numbers | Division Method | Maximum capacity / largest tape |
| LCM of fractions | LCM of numerators / HCF of denominators | Find least number divisible |
| Simultaneous events | Prime Factorisation | Bells toll together / runners |
Prime Factor
(Break down numbers)
Break down numbers
Ex: 12 = 2² × 3
HCF Formula
(Lowest power of common primes)
Lowest power of common primes
Ex: HCF(12, 18) = 6
LCM Formula
(Highest power of all primes)
Highest power of all primes
Ex: LCM(12, 18) = 36
Bell Alarm
(Time interval sync)
Time interval sync
Ex: LCM of 4, 6, 8 sec
Using LCM when finding max container sizeUse HCF for maximum capacity / dividing
Max capacity questions always require HCF, not LCM.
Applying Product rule for 3 numbersProduct = HCF × LCM works only for 2 numbers
Never apply A × B × C = HCF × LCM for three numbers.
Adding remainder before finding LCMFind LCM first, then add the remainder
Always compute LCM of divisors first, then add the required remainder.
Q1.The HCF of two numbers is 12 and their product is 4320. Find their LCM.
Q2.Three bells toll together at intervals of 9, 12, and 15 minutes. After what time will they toll together again?