Example 1
What is the LCM of 40 and 16?
Answer: C) 80
HCF(40, 16) = 8; LCM = 40 × 16 / 8 = 80.
LCM and HCF questions for competitive exams: rules, worked examples and practice
LCM is the smallest number that two or more numbers divide into; HCF is the largest number that divides all of them.
Key rules and formulas
- For two numbers, LCM × HCF = product of the numbers.
- HCF by prime factors: lowest power of each common prime; LCM: highest power of every prime.
- HCF of fractions = HCF of numerators ÷ LCM of denominators.
- Problems on "bells ringing together" or "least number divisible by" need the LCM.
Common traps
- Using the product rule for three numbers (it holds only for two).
- Choosing HCF when the question asks when events coincide (that is LCM).
Where LCM and HCF is asked
- RRB Group D (Mathematics)
- RRB NTPC CBT 1 (Mathematics)
- SSC CGL Tier 1 (Quantitative Aptitude)
- SSC CGL Tier 2 (Mathematical Abilities)
- SSC CHSL Tier 1 (Quantitative Aptitude)
Worked examples
Example 2
What is the LCM of 18 and 45?
Answer: D) 90
HCF(18, 45) = 9; LCM = 18 × 45 / 9 = 90.
Example 3
What is the LCM of 27 and 90?
Answer: C) 270
HCF(27, 90) = 9; LCM = 27 × 90 / 9 = 270.
Frequently asked questions
What is LCM and HCF in competitive exams?
LCM is the smallest number that two or more numbers divide into; HCF is the largest number that divides all of them.
Which exams ask LCM and HCF questions?
On MockBazaar, LCM and HCF questions appear in RRB Group D, RRB NTPC CBT 1, SSC CGL Tier 1, SSC CGL Tier 2, SSC CHSL Tier 1.
What is the most common mistake in LCM and HCF?
Using the product rule for three numbers (it holds only for two).