LCM and HCF — Concepts, Tricks and Placement Questions

LCM and HCF — Concepts, Tricks and Placement Questions

LCM and HCF are two of the most frequently tested topics in aptitude for placements. These concepts appear directly as standalone questions and also underpin problems on time and work, time and distance, and number puzzles. Every placement test includes at least one question from this topic.

Core Definitions

HCF of two numbers is the largest number that divides both of them exactly. LCM of two numbers is the smallest number that is exactly divisible by both. The most important relationship connecting them is: HCF multiplied by LCM equals the product of the two numbers. This identity allows you to find one if the other and the product are known.

Solved Example

Find the HCF and LCM of 36 and 48. Prime factorize 36 as 2 squared multiplied by 3 squared. Prime factorize 48 as 2 to the power 4 multiplied by 3. HCF takes the lowest power of each common factor: 2 squared times 3 equals 12. LCM takes the highest power of each factor: 2 to the power 4 times 3 squared equals 144. Verification: 12 times 144 equals 1728, and 36 times 48 also equals 1728.

Fraction and Co-prime Rules

HCF of fractions equals HCF of numerators divided by LCM of denominators. LCM of fractions equals LCM of numerators divided by HCF of denominators. For consecutive integers n and n plus 1, HCF is always 1 and LCM equals their product. If two numbers are co-prime, their HCF is 1 and their LCM equals their product.

Interview Tips

LCM-based bell ringing problems and HCF-based tile-fitting problems are classic placement questions. For large numbers, use the Euclidean algorithm: HCF of a and b equals HCF of b and a modulo b. Mentioning this algorithm during aptitude discussions signals strong mathematical reasoning to interviewers evaluating your problem-solving approach.