HCF and LCM — 24 Aptitude Questions and Answers with Explanations

HCF and LCM — Questions and Answers

HCF and LCM questions are rarely about finding the HCF of two small numbers — they are about recognising which one the situation calls for. "Greatest number that divides…" means HCF; "least number divisible by…" means LCM. The remainder variants (same remainder, different remainders) each have a fixed one-line technique worth memorising.

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HCF and LCM— Concepts, Formulas & Shortcuts

HCF × LCM = product of the two numbers (true for exactly two numbers).
"Greatest number that divides x, y, z" → HCF. "Least number divisible by x, y, z" → LCM.
Least number leaving remainder r with each divisor = LCM + r.
Greatest number leaving the SAME remainder = HCF of the differences of the numbers.
If numbers are in ratio a : b with HCF h, the numbers are ah and bh and the LCM is abh.
HCF of fractions = HCF(numerators)/LCM(denominators); LCM of fractions = LCM(numerators)/HCF(denominators).

HCF and LCM Practice Questions with Answers

Attempt each question first, then open the explanation. All 24 questions below are free to read and require no signup.

Q1.The HCF of 24 and 36 is:
Easy
- A6
- B8
- C12
- D18
+Show Answer & Explanation
Answer: C. 12
Explanation: 24 = 2³ × 3, 36 = 2² × 3² → common = 2² × 3 = 12.
HCF and LCM question 1 of 24
Q2.The LCM of 12, 15 and 20 is:
Easy
- A30
- B48
- C60
- D120
+Show Answer & Explanation
Answer: C. 60
Explanation: 12 = 2²·3, 15 = 3·5, 20 = 2²·5 → LCM = 2² × 3 × 5 = 60.
HCF and LCM question 2 of 24
Q3.The product of two numbers is 2,028 and their HCF is 13. Their LCM is:
Easy
- A26
- B78
- C156
- D169
+Show Answer & Explanation
Answer: C. 156
Explanation: LCM = product/HCF = 2028/13 = 156.
HCF and LCM question 3 of 24
Q4.The greatest number that divides 43, 91 and 183 leaving the same remainder in each case is:
Difficult
- A4
- B7
- C9
- D13
+Show Answer & Explanation
Answer: A. 4
Explanation: Differences: 91 − 43 = 48, 183 − 91 = 92, 183 − 43 = 140. HCF(48, 92, 140) = 4.
HCF and LCM question 4 of 24
Q5.The least number which when divided by 6, 7 and 8 leaves a remainder 3 in each case is:
Moderate
- A165
- B168
- C171
- D175
+Show Answer & Explanation
Answer: C. 171
Explanation: LCM(6,7,8) = 168 → required number = 168 + 3 = 171.
HCF and LCM question 5 of 24
Q6.The HCF of two numbers is 11 and their LCM is 7,700. If one number is 275, the other is:
Moderate
- A288
- B308
- C318
- D330
+Show Answer & Explanation
Answer: B. 308
Explanation: Other = (11 × 7700)/275 = 84700/275 = 308.
HCF and LCM question 6 of 24
Q7.The smallest number exactly divisible by 12, 16, 18 and 21 is:
Moderate
- A504
- B1,008
- C1,512
- D2,016
+Show Answer & Explanation
Answer: B. 1,008
Explanation: LCM = 2⁴ × 3² × 7 = 1,008.
HCF and LCM question 7 of 24
Q8.Two numbers are in the ratio 3 : 4 and their HCF is 4. Their LCM is:
Moderate
- A24
- B36
- C48
- D96
+Show Answer & Explanation
Answer: C. 48
Explanation: The numbers are 12 and 16 → LCM = 48 (equivalently 3 × 4 × 4).
HCF and LCM question 8 of 24
Q9.The HCF of 18 and 30 is:
Easy
- A3
- B6
- C9
- D15
+Show Answer & Explanation
Answer: B. 6
Explanation: 18 = 2 × 3², 30 = 2 × 3 × 5 → common = 2 × 3 = 6.
HCF and LCM question 9 of 24
Q10.The LCM of 8 and 12 is:
Easy
- A16
- B24
- C36
- D48
+Show Answer & Explanation
Answer: B. 24
Explanation: 8 = 2³, 12 = 2² × 3 → LCM = 2³ × 3 = 24.
HCF and LCM question 10 of 24
Q11.The HCF of two co-prime numbers is always:
Easy
- A0
- B1
- Ctheir product
- Dthe smaller number
+Show Answer & Explanation
Answer: B. 1
Explanation: Co-prime numbers share no common factor other than 1.
HCF and LCM question 11 of 24
Q12.The greatest number that divides 60, 84 and 108 exactly is:
Moderate
- A6
- B12
- C18
- D24
+Show Answer & Explanation
Answer: B. 12
Explanation: HCF(60, 84, 108) = 12.
HCF and LCM question 12 of 24
Q13.The least number which when divided by 5, 6 and 8 leaves a remainder 2 is:
Moderate
- A118
- B120
- C122
- D125
+Show Answer & Explanation
Answer: C. 122
Explanation: LCM(5, 6, 8) = 120 → required number = 120 + 2 = 122.
HCF and LCM question 13 of 24
Q14.Three bells ring at intervals of 6, 8 and 12 minutes. If they ring together at 9:00 am, they will next ring together at:
Moderate
- A9:12 am
- B9:24 am
- C9:36 am
- D9:48 am
+Show Answer & Explanation
Answer: B. 9:24 am
Explanation: LCM(6, 8, 12) = 24 minutes → they next coincide at 9:24 am.
HCF and LCM question 14 of 24
Q15.The LCM of two numbers is 48 and their HCF is 4. If one number is 12, the other is:
Moderate
- A8
- B12
- C16
- D24
+Show Answer & Explanation
Answer: C. 16
Explanation: Product = HCF × LCM = 4 × 48 = 192 → other = 192/12 = 16.
HCF and LCM question 15 of 24
Q16.The HCF of 1/2, 3/4 and 5/6 is:
Difficult
- A1/2
- B1/12
- C1/6
- D5/12
+Show Answer & Explanation
Answer: B. 1/12
Explanation: HCF of fractions = HCF(numerators)/LCM(denominators) = HCF(1,3,5)/LCM(2,4,6) = 1/12.
HCF and LCM question 16 of 24
Q17.The HCF of 12 and 20 is:
Easy
- A2
- B4
- C6
- D10
+Show Answer & Explanation
Answer: B. 4
Explanation: 12 = 2²·3, 20 = 2²·5 → HCF = 4.
HCF and LCM question 17 of 24
Q18.The LCM of 6 and 10 is:
Easy
- A16
- B20
- C30
- D60
+Show Answer & Explanation
Answer: C. 30
Explanation: 6 = 2·3, 10 = 2·5 → LCM = 2 × 3 × 5 = 30.
HCF and LCM question 18 of 24
Q19.The HCF of 15, 25 and 35 is:
Easy
- A3
- B5
- C7
- D15
+Show Answer & Explanation
Answer: B. 5
Explanation: All three share only the factor 5.
HCF and LCM question 19 of 24
Q20.The LCM of 4, 6 and 10 is:
Moderate
- A30
- B40
- C60
- D120
+Show Answer & Explanation
Answer: C. 60
Explanation: LCM = 2² × 3 × 5 = 60.
HCF and LCM question 20 of 24
Q21.The greatest number that divides 90 and 126 exactly is:
Moderate
- A6
- B12
- C18
- D24
+Show Answer & Explanation
Answer: C. 18
Explanation: 90 = 2·3²·5 and 126 = 2·3²·7 → HCF = 2 × 9 = 18.
HCF and LCM question 21 of 24
Q22.Two numbers have HCF 6 and LCM 36. If one number is 12, the other is:
Moderate
- A12
- B18
- C24
- D36
+Show Answer & Explanation
Answer: B. 18
Explanation: Product = 6 × 36 = 216 → other = 216/12 = 18.
HCF and LCM question 22 of 24
Q23.The smallest number divisible by 8, 10 and 12 is:
Moderate
- A80
- B100
- C120
- D240
+Show Answer & Explanation
Answer: C. 120
Explanation: LCM(8, 10, 12) = 120.
HCF and LCM question 23 of 24
Q24.Two bells ring every 15 and 20 minutes. If they ring together at noon, they next ring together at:
Moderate
- A12:30
- B12:45
- C1:00
- D1:15
+Show Answer & Explanation
Answer: C. 1:00
Explanation: LCM(15, 20) = 60 minutes → they coincide again at 1:00.
HCF and LCM question 24 of 24

HCF and LCM — Frequently Asked Questions

How do I find the greatest number that leaves the same remainder?+

Take the pairwise differences of the given numbers and find their HCF. For 43, 91 and 183 the differences are 48, 92 and 140, whose HCF is 4.

Does HCF × LCM = product work for three numbers?+

No. It holds only for two numbers. For three or more, compute the HCF and LCM separately by prime factorisation.

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