Practice Questions
HCF (Highest Common Factor)
The largest number that divides each of the given numbers exactly. Found via prime factorisation: take lowest powers of common primes.
LCM (Least Common Multiple)
The smallest number divisible by each given number. Take highest powers of all primes involved.
Key Relation
For two numbers a and b: HCF(a,b) × LCM(a,b) = a × b.
Methods
- Prime factorisation
- Division method (for HCF)
- Listing multiples (for small numbers)
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Q1 Easy
Find the HCF of 24 and 36.
Explanation24 = 2³×3, 36 = 2²×3². HCF = 2²×3 = 12. -
Q2 Easy
Find the LCM of 8 and 12.
Explanation8 = 2³, 12 = 2²×3. LCM = 2³×3 = 24. -
Q3 Easy
HCF of 15 and 25 is:
Explanation15 = 3×5, 25 = 5². HCF = 5. -
Q4 Easy
LCM of 9 and 12 is:
Explanation9 = 3², 12 = 2²×3. LCM = 2²×3² = 36. -
Q5 Medium
If HCF(a,b)=4 and LCM(a,b)=60, and a=12, find b.
Explanationa×b = HCF×LCM → 12×b = 4×60 = 240 → b = 20. -
Q6 Medium
HCF of 48, 72 and 96 is:
Explanation48=2⁴×3, 72=2³×3², 96=2⁵×3. HCF = 2³×3 = 24. -
Q7 Hard
Two numbers are in ratio 3:4 and their LCM is 84. The numbers are:
ExplanationNumbers 3k and 4k. LCM(3k,4k)=12k=84 → k=7. Numbers: 21 and 28.
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Q8 Easy
LCM of two co-prime numbers 7 and 11 is:
ExplanationCo-prime numbers: LCM = product = 7×11 = 77. -
Q9 Hard
HCF of 0.5 and 1.25 (as fractions) is:
Explanation0.5 = 1/2, 1.25 = 5/4. HCF of fractions = HCF(numerators)/LCM(denominators) = 1/4 = 0.25. -
Q10 Medium
The least number which when divided by 6, 8 and 12 leaves remainder 0 is:
ExplanationRequired number is LCM(6,8,12) = 24. -
Q11 Medium
If HCF(x,18)=6 and LCM(x,18)=54, find x.
Explanationx×18 = 6×54 = 324 → x = 18. -
Q12 Easy
Three bells ring at intervals of 6, 8 and 12 seconds. Together again after:
ExplanationLCM(6,8,12) = 24 seconds. -
Q13 Medium
HCF of (2³×3²×5) and (2²×3×7) is:
ExplanationTake lowest powers of common primes: 2² × 3 = 4 × 3 = 12. -
Q14 Medium
Product of two numbers is 216 and HCF is 6. LCM is:
ExplanationLCM = product/HCF = 216/6 = 36.
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DS1 Easy
What is the HCF of A and B?
Statement IA = 48 and B = 72.
Statement IIHCF(A, B) = 24.
ExplanationStatement I alone determines HCF = 24. Statement II repeats the answer without defining A and B. -
DS2 Easy
What is the LCM of 9 and 12?
Statement ILCM(9, 12) = 36.
Statement II9 and 12 are co-prime.
ExplanationLCM is 36 from Statement I. Statement II is false (they share factor 3), so it adds nothing.
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DS3 Medium
Two numbers are in ratio 2:3. What is their LCM?
Statement IThe numbers are 14 and 21.
Statement IITheir HCF is 7.
ExplanationRatio 2:3 with HCF 7 gives numbers 14 and 21. Either statement alone is insufficient; together they fix the pair and LCM = 42. -
DS4 Medium
What is the HCF of three numbers?
Statement IThe numbers are 24, 36 and 60.
Statement IIEach number is divisible by 12.
ExplanationHCF(24, 36, 60) = 12 from Statement I. Statement II only says 12 divides each — HCF could still be 12 or a divisor of 12 without the actual numbers.