LCM & HCF – Number Systems | General Aptitude for GATE, PSU, ESE, AE/JE

LCM (Least Common Multiple) and HCF (Highest Common Factor) are important concepts in Number Systems and are frequently asked in competitive exams like GATE, PSU, ESE, AE/JE.

What is HCF?

HCF (Highest Common Factor) is the greatest number that divides all given numbers exactly.

Example:
HCF of 12 and 18:
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18
Common factors = 1, 2, 3, 6
HCF = 6

What is LCM?

LCM (Least Common Multiple) is the smallest number that is divisible by all given numbers.

Example:
Multiples of 4 = 4, 8, 12, 16...
Multiples of 6 = 6, 12, 18...
LCM = 12

Methods to Find HCF & LCM

Prime Factorization Method

Example: Find HCF and LCM of 24 and 36

24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3

• HCF: 2 × 2 × 3 = 12
• LCM: 2 × 2 × 2 × 3 × 3 = 72

Important Formula

LCM × HCF = Product of Numbers

Example:
For 12 and 18:
HCF = 6, LCM = 36
6 × 36 = 216 = 12 × 18

Key Properties

• HCF of co-prime numbers = 1
• LCM of co-prime numbers = product of numbers
• HCF is always less than or equal to LCM

Practice Questions

• Find HCF of 16 and 24
• Find LCM of 15 and 20
• Find HCF and LCM of 18, 24, 30
• If HCF = 4 and product = 240, find LCM

Conclusion

LCM and HCF help solve problems quickly in aptitude exams. Strong understanding of these concepts improves speed and accuracy in exams like GATE, PSU, and ESE.

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