How many three-digit integers are divisible by both 18 and 24?

LCM(18, 24) = 72. Count = floor(999 ÷ 72) − floor(99 ÷ 72) = 13 − 1 = 12.

The greatest divisor that leaves remainders 8 and 14 on dividing 968 and 1358 is d. What remainder does 2026 leave when divided by d?

d = HCF(960, 1344) = 192. Since 2026 = 192 × 10 + 106, the remainder is 106.

Which greatest integer gives an equal remainder when 345, 513 and 765 are divided by it?

Take HCF(513 − 345, 765 − 513) = HCF(168, 252) = 84.

What is the least non-negative integer to subtract from 2867 to make it divisible by 12, 18 and 27?

LCM(12, 18, 27) = 108. Since 2867 = 108 × 26 + 59, subtract 59.

Three bells ring every 18, 30 and 42 seconds. Starting with a simultaneous ringing, how many simultaneous ringings occur in 63 minutes, including both endpoints?

Common interval = LCM(18, 30, 42) = 630 seconds. Including the initial ringing gives 63 × 60 ÷ 630 + 1 = 7.

Find the HCF of 2.25 and 3.75.

HCF(225, 375) = 75. Restore two decimal places to obtain 0.75.

Find the HCF of 2^6 × 3³ × 5 and 2^4 × 3² × 7.

Use the lower powers of common primes: 2^4 × 3² = 144.

A library has 315 Punjabi, 405 Hindi and 495 English books. Each stack has the same maximum number of books and contains one language only. How many stacks are formed?

Maximum books per stack = HCF(315, 405, 495) = 45. Stacks = (315 + 405 + 495) ÷ 45 = 27.

Find the least integer greater than 100 that leaves remainder 9 when divided by 25, 30 and 40.

LCM(25, 30, 40) = 600. The first suitable number above 100 is 600 + 9 = 609.

What is the LCM of 44 and 66?

HCF(44, 66) = 22. Hence LCM = 44 × 66 ÷ 22 = 132.

After removing 6 damaged pens from 486 pens and 10 damaged pencils from 730 pencils, identical kits are made using all remaining items. If the number of kits is as large as possible, how many more pencils than pens are in each kit?

Usable totals are 480 and 720, giving HCF = 240 kits. Each kit has 2 pens and 3 pencils, so the difference is 1.

A rectangular sheet 154 cm by 210 cm is cut into the largest possible equal squares without waste. What is the perimeter of each square in cm?

Largest square side = HCF(154, 210) = 14 cm. Perimeter = 4 × 14 = 56 cm.

Three maintenance jobs recur every 8, 12 and 18 days. All are done today. After how many days will they next fall on the same day?

The first common recurrence is LCM(8, 12, 18) = 72 days.

The HCF and LCM of two positive integers are 32 and 960. If one integer is 160, find the other.

Their product is 32 × 960. The other integer is 32 × 960 ÷ 160 = 192.

A number divides 733, 1027 and 1319 leaving remainders 13, 19 and 23 respectively. Find its greatest possible value.

Subtract the respective remainders to get 720, 1008 and 1296. Their HCF is 144.

Two positive integers have HCF 19. Their sum is 228 and their ratio is less than 1 when the smaller is written first. What is the greatest possible value of the smaller integer?

Write the numbers as 19a and 19b, so a + b = 12 and a, b are co-prime. The closest eligible pair is (5, 7), making the smaller integer 19 × 5 = 95.

For positive integers x, y and z, LCM(x, y) = y and HCF(y, z) = y. If z = 630, what is LCM(x, y, z)?

The first condition gives x divides y; the second gives y divides z. Thus all three divide z, and their LCM is z = 630.

A divisor d greater than 10 leaves the same remainder when dividing 250, 394 and 610. How many possible values of d are there?

d must divide HCF(144, 216) = 72. Its factors above 10 are 12, 18, 24, 36 and 72, giving 5 values.

A trader has ₹7643. What is the least amount in ₹ that must be added so the total can be paid in equal instalments of ₹84, ₹126 or ₹210 without a balance?

LCM(84, 126, 210) = 1260. The next multiple after 7643 is 8820, so add 8820 − 7643 = ₹1177.

Find the least integer greater than 50 that leaves remainder 2 when divided by 16 and 24.

The numbers are 48k + 2. Since 50 is excluded, the next is 96 + 2 = 98.

Find the least perfect square divisible by 24, 40 and 60.

LCM = 120 = 2³ × 3 × 5. Make every prime exponent even by multiplying by 2 × 3 × 5, giving 3600.

What is the HCF of 8/9, 10/27 and 14/45?

HCF of numerators = 2 and LCM of denominators = 135. Thus HCF = 2/135.

Two numbers are in the ratio 12:18 and their HCF is 25. Find their LCM.

Reduce 12:18 to 2:3, giving numbers 50 and 75. Their LCM is 25 × 2 × 3 = 150.

Data sufficiency: How many unordered pairs of positive integers have HCF 16 and sum S? I. S is a multiple of 16. II. S = 304.

Statement II alone is sufficient; Statement I alone is not.. I gives no fixed S: S = 32 gives 1 pair, while S = 304 gives 9. II fixes a + b = 304 ÷ 16 = 19 after removing the HCF, giving 9 co-prime unordered pairs, so II alone is sufficient.

What is the smallest five-digit integer that leaves remainder 4 when divided by 18, 24 and 30?

The integer is 360k + 4. The first value at least 10000 is 360 × 28 + 4 = 10084.

Topic

HCF and LCM of Numbers MCQ – Part 3 - Topic Guide and MCQs

Part of Quantitative Aptitude > 02 HCF And LCM Of Numbers - 25 questions, about 25 min, with an explanation after every answer.

Question count

about 25 min

Estimated time

Mixed

Difficulty

03 Nov 2026

Last updated

Quick answer

HCF and LCM of Numbers MCQ – Part 3 is a topic inside Quantitative Aptitude (02 HCF And LCM Of Numbers). It runs 25 untimed MCQs - roughly 25 min - and the review explains every answer once you submit.

Topic introduction

What HCF and LCM of Numbers MCQ – Part 3 covers

The shape of the set before you start it.

HCF and LCM of Numbers MCQ – Part 3 sits inside Quantitative Aptitude, under the 02 HCF And LCM Of Numbers lane, and the portal keeps it as one self-contained set: 25 questions, four options each, no clock and a written explanation behind every answer.

Attempt it once to find the gaps, read why each distractor is wrong, then retake the same set a few days later. The questions you miss twice are the ones worth writing down.

Curated by Gurpreet Singh · Punjab Police SI, Rank 2 (713/800) · Founder, House of Aspirants · Read his story →

Question bank

HCF and LCM of Numbers MCQ – Part 3: all 25 questions

Read the question, pick an option, then open the answer.

How many three-digit integers are divisible by both 18 and 24?
1. 14
2. 12
3. 11
4. 13
Show answer

Answer: (B) 12

Explanation: LCM(18, 24) = 72. Count = floor(999 ÷ 72) − floor(99 ÷ 72) = 13 − 1 = 12.
The greatest divisor that leaves remainders 8 and 14 on dividing 968 and 1358 is d. What remainder does 2026 leave when divided by d?
1. 86
2. 192
3. 10
4. 106
Show answer

Answer: (D) 106

Explanation: d = HCF(960, 1344) = 192. Since 2026 = 192 × 10 + 106, the remainder is 106.
Which greatest integer gives an equal remainder when 345, 513 and 765 are divided by it?
1. 84
2. 12
3. 168
4. 42
Show answer

Answer: (A) 84

Explanation: Take HCF(513 − 345, 765 − 513) = HCF(168, 252) = 84.
What is the least non-negative integer to subtract from 2867 to make it divisible by 12, 18 and 27?
1. 5
2. 108
3. 59
4. 49
Show answer

Answer: (C) 59

Explanation: LCM(12, 18, 27) = 108. Since 2867 = 108 × 26 + 59, subtract 59.
Three bells ring every 18, 30 and 42 seconds. Starting with a simultaneous ringing, how many simultaneous ringings occur in 63 minutes, including both endpoints?
1. 6
2. 7
3. 8
4. 10
Show answer

Answer: (B) 7

Explanation: Common interval = LCM(18, 30, 42) = 630 seconds. Including the initial ringing gives 63 × 60 ÷ 630 + 1 = 7.
Find the HCF of 2.25 and 3.75.
1. 0.15
2. 7.5
3. 1.5
4. 0.75
Show answer

Answer: (D) 0.75

Explanation: HCF(225, 375) = 75. Restore two decimal places to obtain 0.75.
Find the HCF of 2^6 × 3³ × 5 and 2^4 × 3² × 7.
1. 432
2. 720
3. 144
4. 1008
Show answer

Answer: (C) 144

Explanation: Use the lower powers of common primes: 2^4 × 3² = 144.
A library has 315 Punjabi, 405 Hindi and 495 English books. Each stack has the same maximum number of books and contains one language only. How many stacks are formed?
1. 45
2. 81
3. 27
4. 9
Show answer

Answer: (C) 27

Explanation: Maximum books per stack = HCF(315, 405, 495) = 45. Stacks = (315 + 405 + 495) ÷ 45 = 27.
Find the least integer greater than 100 that leaves remainder 9 when divided by 25, 30 and 40.
1. 600
2. 309
3. 1209
4. 609
Show answer

Answer: (D) 609

Explanation: LCM(25, 30, 40) = 600. The first suitable number above 100 is 600 + 9 = 609.
What is the LCM of 44 and 66?
1. 22
2. 264
3. 132
4. 2904
Show answer

Answer: (C) 132

Explanation: HCF(44, 66) = 22. Hence LCM = 44 × 66 ÷ 22 = 132.
After removing 6 damaged pens from 486 pens and 10 damaged pencils from 730 pencils, identical kits are made using all remaining items. If the number of kits is as large as possible, how many more pencils than pens are in each kit?
1. 240
2. 1
3. 2
4. 3
Show answer

Answer: (B) 1

Explanation: Usable totals are 480 and 720, giving HCF = 240 kits. Each kit has 2 pens and 3 pencils, so the difference is 1.
A rectangular sheet 154 cm by 210 cm is cut into the largest possible equal squares without waste. What is the perimeter of each square in cm?
1. 56
2. 196
3. 14
4. 28
Show answer

Answer: (A) 56

Explanation: Largest square side = HCF(154, 210) = 14 cm. Perimeter = 4 × 14 = 56 cm.
Three maintenance jobs recur every 8, 12 and 18 days. All are done today. After how many days will they next fall on the same day?
1. 36
2. 48
3. 72
4. 144
Show answer

Answer: (C) 72

Explanation: The first common recurrence is LCM(8, 12, 18) = 72 days.
The HCF and LCM of two positive integers are 32 and 960. If one integer is 160, find the other.
1. 240
2. 480
3. 192
4. 96
Show answer

Answer: (C) 192

Explanation: Their product is 32 × 960. The other integer is 32 × 960 ÷ 160 = 192.
A number divides 733, 1027 and 1319 leaving remainders 13, 19 and 23 respectively. Find its greatest possible value.
1. 72
2. 48
3. 288
4. 144
Show answer

Answer: (D) 144

Explanation: Subtract the respective remainders to get 720, 1008 and 1296. Their HCF is 144.
Two positive integers have HCF 19. Their sum is 228 and their ratio is less than 1 when the smaller is written first. What is the greatest possible value of the smaller integer?
1. 114
2. 57
3. 76
4. 95
Show answer

Answer: (D) 95

Explanation: Write the numbers as 19a and 19b, so a + b = 12 and a, b are co-prime. The closest eligible pair is (5, 7), making the smaller integer 19 × 5 = 95.
For positive integers x, y and z, LCM(x, y) = y and HCF(y, z) = y. If z = 630, what is LCM(x, y, z)?
1. 630
2. 1890
3. 1260
4. 315
Show answer

Answer: (A) 630

Explanation: The first condition gives x divides y; the second gives y divides z. Thus all three divide z, and their LCM is z = 630.
A divisor d greater than 10 leaves the same remainder when dividing 250, 394 and 610. How many possible values of d are there?
1. 12
2. 6
3. 5
4. 7
Show answer

Answer: (C) 5

Explanation: d must divide HCF(144, 216) = 72. Its factors above 10 are 12, 18, 24, 36 and 72, giving 5 values.
A trader has ₹7643. What is the least amount in ₹ that must be added so the total can be paid in equal instalments of ₹84, ₹126 or ₹210 without a balance?
1. 1177
2. 83
3. 337
4. 1259
Show answer

Answer: (A) 1177

Explanation: LCM(84, 126, 210) = 1260. The next multiple after 7643 is 8820, so add 8820 − 7643 = ₹1177.
Find the least integer greater than 50 that leaves remainder 2 when divided by 16 and 24.
1. 48
2. 98
3. 50
4. 146
Show answer

Answer: (B) 98

Explanation: The numbers are 48k + 2. Since 50 is excluded, the next is 96 + 2 = 98.
Find the least perfect square divisible by 24, 40 and 60.
1. 120
2. 1800
3. 14400
4. 3600
Show answer

Answer: (D) 3600

Explanation: LCM = 120 = 2³ × 3 × 5. Make every prime exponent even by multiplying by 2 × 3 × 5, giving 3600.
What is the HCF of 8/9, 10/27 and 14/45?
1. 2/9
2. 2/135
3. 280/3
4. 1/135
Show answer

Answer: (B) 2/135

Explanation: HCF of numerators = 2 and LCM of denominators = 135. Thus HCF = 2/135.
Two numbers are in the ratio 12:18 and their HCF is 25. Find their LCM.
1. 150
2. 300
3. 75
4. 900
Show answer

Answer: (A) 150

Explanation: Reduce 12:18 to 2:3, giving numbers 50 and 75. Their LCM is 25 × 2 × 3 = 150.
Data sufficiency: How many unordered pairs of positive integers have HCF 16 and sum S? I. S is a multiple of 16. II. S = 304.
1. Statement II alone is sufficient; Statement I alone is not.
2. Both statements together are sufficient, but neither alone is sufficient.
3. Statement I alone is sufficient; Statement II alone is not.
4. Each statement alone is sufficient.
Show answer

Answer: (A) Statement II alone is sufficient; Statement I alone is not.

Explanation: I gives no fixed S: S = 32 gives 1 pair, while S = 304 gives 9. II fixes a + b = 304 ÷ 16 = 19 after removing the HCF, giving 9 co-prime unordered pairs, so II alone is sufficient.
What is the smallest five-digit integer that leaves remainder 4 when divided by 18, 24 and 30?
1. 9724
2. 10084
3. 10080
4. 10444
Show answer

Answer: (B) 10084

Explanation: The integer is 360k + 4. The first value at least 10000 is 360 × 28 + 4 = 10084.

Why it matters

Why HCF and LCM of Numbers MCQ – Part 3 is worth the hours

Where the marks actually come from.

HCF and LCM of Numbers MCQ – Part 3 is factual rather than analytical: you either recall it in seconds or you lose the mark to somebody who did. That makes it one of the cheapest sections to convert - a handful of short sittings usually settles the whole cluster.

Exam relevance

Exams where HCF and LCM of Numbers MCQ – Part 3 matters

Derived from the subject and lane this topic belongs to.

Punjab Police Constable

The highest-volume recruitment on this list. Build your base with Punjab GK and current affairs, then drill reasoning until speed is automatic.

Punjab Police ASI

Assistant Sub-Inspector papers separate candidates on English and Punjabi accuracy as much as on general awareness. Practise language daily.

Punjab Police Sub-Inspector (SI)

The most competitive paper here. Polity, history and quant reasoning decide the rank - so take full timed mocks before the exam.

Punjab Police Intelligence Assistant

Data handling, mental ability and computer awareness carry most of the weight. Use short topic sets and check every explanation.

Punjab Police Jail Warder

A tighter syllabus: general awareness, Punjabi and basic reasoning. Perfect for a daily quiz habit - short sessions, high consistency.

Patwari

Revenue work starts with Punjab geography, history and current affairs. Add quant for the sections that reward calculation speed.

Excise Inspector

General awareness and English carry this paper. Track Punjab policy news daily and revise it as MCQs, not as notes.

Naib Tehsildar

Land records, Punjab history and polity, plus data interpretation. A strong polity base is the fastest score to build.

Clerk

Grammar, comprehension, typing and basic computer knowledge. Accuracy beats speed here - review every wrong answer.

PSPCL jobs

Recruitment by the Punjab State Power Corporation Limited. Technical aptitude sits alongside general awareness and reasoning.

Punjab Police Head Constable

The communication and clerical tier of Punjab Police. Punjabi, English and general knowledge carry the paper, and computer awareness is worth real marks.

Staff Selection Commission

The central recruitment ladder most aspirants attempt alongside a state paper. Arithmetic, reasoning and English decide the score; general awareness decides the cutoff.

Railway Recruitment

A high-volume, high-speed paper. Arithmetic, reasoning and general awareness asked at a pace that punishes anyone still working out method during the attempt.

Banking Exams

Quantitative aptitude and reasoning at speed, with a separate English section and a general awareness paper that moves with the financial news cycle.

Expected questions

Expected questions from HCF and LCM of Numbers MCQ – Part 3

What an examiner usually reaches for in this cluster.

Expect one-line recall questions - definitions, stand-for expansions, identifiers and the ordering of things. Practise the wording as well as the concept: these papers test terminology, and the set above uses the same four-option shape they do.

Daily habit

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20 fresh mixed questions a day, plus the current-affairs sets examiners keep reusing.

Daily Quiz Expected MCQs

Previous year questions

Previous Year Questions

How this topic behaves in real papers.

Past papers reuse clusters like this almost verbatim across years and posts. Run the same set until every distractor is familiar - previous-year style questions stop being recall and start being free marks.

Where the previous-year sets live

The portal's previous-year practice runs through the General Knowledge lane and the daily mixed quiz.

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HCF and LCM of Numbers MCQ – Part 3 - common questions

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How long is the HCF and LCM of Numbers MCQ – Part 3 quiz?

HCF and LCM of Numbers MCQ – Part 3 runs 25 untimed questions - about 25 min at a steady pace. The set clears at 40% and you can retake it as often as you like.

What kind of questions does HCF and LCM of Numbers MCQ – Part 3 ask?

The set answers that: each question carries four options and a full explanation, so you learn the wording an examiner uses, not just the fact behind it.

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