What is the greatest integer that leaves the same remainder when dividing 157, 229 and 373?

Take the HCF of differences: HCF(229 − 157, 373 − 229) = HCF(72, 144) = 72.

Harleen and Simran start together from the same point on a circular track. Their lap times are 75 and 90 seconds. After how many minutes will both first return together to the starting point?

LCM(75, 90) = 450 seconds. Thus the time is 450 ÷ 60 = 7.5 minutes.

Data sufficiency: What is the sum of two positive integers? I. Their HCF is 18 and LCM is 540. II. Both integers are at least 90.

Both statements together are sufficient, but neither alone is sufficient.. I gives co-prime factor pairs of 30 after dividing both integers by 18, so several sums are possible. Together with II, only (90, 108) remains, giving sum 198; II alone gives no unique sum.

Find the least positive integer that leaves remainders 7, 11 and 19 when divided by 12, 16 and 24 respectively.

Each remainder is 5 less than its divisor. Hence the number is LCM(12, 16, 24) − 5 = 48 − 5 = 43.

A school has 216 pencils and 288 erasers. It makes the maximum number of identical gift packets using everything. How many items are in each packet?

Maximum packets = HCF(216, 288) = 72. Each contains 216 ÷ 72 + 288 ÷ 72 = 7 items.

Three bells ring every 14, 21 and 35 seconds. They ring together now. How many simultaneous ringings occur in the next 35 minutes, excluding now but including the endpoint?

They ring together every LCM(14, 21, 35) = 210 seconds. Excluding the initial ringing, the count is 35 × 60 ÷ 210 = 10.

Find the least positive integer that leaves remainder 3 when divided by 8, 12 and 20, and is divisible by 7.

The number is 120k + 3. Modulo 7 this is k + 3, so the least suitable k is 4 and the number is 483.

If a = 2^5 × 3² × 7 and b = 2³ × 3^4 × 5, find LCM(a, b) ÷ HCF(a, b).

Cancel the common lowest powers. The ratio is 2² × 3² × 5 × 7 = 1260.

A largest possible divisor d leaves the same remainder r on dividing 613, 853 and 1213. Find d + r.

d = HCF(240, 360) = 120. Since 613 = 120 × 5 + 13, d + r = 120 + 13 = 133.

Three traffic signals change every 40, 56 and 70 seconds. They change together at 9:10:00 a.m. At what time do they next change together?

LCM(40, 56, 70) = 280 seconds = 4 minutes 40 seconds. Add this to 9:10:00 to get 9:14:40.

What is the least non-negative integer to add to 754 to make it divisible by both 18 and 24?

LCM(18, 24) = 72, and 754 leaves remainder 34. Add 72 − 34 = 38.

A shop has 378 kg rice, 462 kg wheat and 630 kg maize. Each grain is packed separately in bags of the same maximum capacity, with nothing left. How many bags are needed in total?

Maximum capacity = HCF(378, 462, 630) = 42 kg. Total bags = (378 + 462 + 630) ÷ 42 = 35.

What is the least non-negative integer to subtract from 9876 so that the result is divisible by 14, 21 and 30?

LCM(14, 21, 30) = 210. Since 9876 = 210 × 47 + 6, subtract 6.

A rectangular floor measures 6.72 m by 4.80 m. What is the minimum number of equal square tiles needed to cover it without cutting?

Largest tile side = HCF(672, 480) = 96 cm. Minimum tiles = (672 ÷ 96) × (480 ÷ 96) = 35.

Find the HCF of 168, 252 and 420.

HCF(168, 252) = 84, and 420 = 84 × 5. Hence the required HCF is 84.

The greatest divisor of 1099, 1440 and 1788 leaving remainders 11, 12 and 20 respectively is d. Find d − 20.

d = HCF(1088, 1428, 1768) = 68. Therefore d − 20 = 48.

What is the smallest four-digit integer divisible by 16, 20 and 28?

LCM(16, 20, 28) = 560. The first multiple at least 1000 is 560 × 2 = 1120.

What is the LCM of 5/12, 7/18 and 11/24?

For reduced fractions, LCM = LCM of numerators ÷ HCF of denominators = 385/6.

The ratio of two positive integers is 6:10 and their LCM exceeds their HCF by 308. Find the smaller integer.

Reduce the ratio to 3:5. If the HCF is h, then 15h − h = 308, giving h = 22 and the smaller number 3 × 22 = 66.

What is the LCM of 28, 42 and 70?

Take the highest prime powers: 2² × 3 × 5 × 7 = 420.

Find the greatest integer that divides 879 and 1246 leaving remainders 9 and 16 respectively.

The divisor must divide 879 − 9 = 870 and 1246 − 16 = 1230. Their HCF is 30.

Two numbers are in the ratio 7:9 and their HCF is 16. What is their sum?

Since 7 and 9 are co-prime, the numbers are 16 × 7 and 16 × 9. Their sum is 16 × 16 = 256.

Find the HCF of 0.84, 1.26 and 2.10.

HCF(84, 126, 210) = 42. Restore two decimal places to get 0.42.

The ratio of two numbers is 5:8 and their LCM is 680. Find their difference.

Write the numbers as 5x and 8x. Then 40x = 680, so their difference is 3 × 17 = 51.

Find the least integer greater than 20 that leaves remainder 4 when divided by 6, 10 and 15.

Such numbers are 30k + 4 because LCM(6, 10, 15) = 30. The first above 20 is 34.

Topic

HCF and LCM of Numbers MCQ – Part 1 - 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 1 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 1 covers

The shape of the set before you start it.

HCF and LCM of Numbers MCQ – Part 1 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 1: all 25 questions

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

What is the greatest integer that leaves the same remainder when dividing 157, 229 and 373?
1. 72
2. 36
3. 12
4. 144
Show answer

Answer: (A) 72

Explanation: Take the HCF of differences: HCF(229 − 157, 373 − 229) = HCF(72, 144) = 72.
Harleen and Simran start together from the same point on a circular track. Their lap times are 75 and 90 seconds. After how many minutes will both first return together to the starting point?
1. 7.5
2. 15
3. 2.5
4. 5
Show answer

Answer: (A) 7.5

Explanation: LCM(75, 90) = 450 seconds. Thus the time is 450 ÷ 60 = 7.5 minutes.
Data sufficiency: What is the sum of two positive integers? I. Their HCF is 18 and LCM is 540. II. Both integers are at least 90.
1. Each statement alone is sufficient.
2. Both statements together are sufficient, but neither alone is sufficient.
3. Statement I alone is sufficient; Statement II alone is not.
4. Statement II alone is sufficient; Statement I alone is not.
Show answer

Answer: (B) Both statements together are sufficient, but neither alone is sufficient.

Explanation: I gives co-prime factor pairs of 30 after dividing both integers by 18, so several sums are possible. Together with II, only (90, 108) remains, giving sum 198; II alone gives no unique sum.
Find the least positive integer that leaves remainders 7, 11 and 19 when divided by 12, 16 and 24 respectively.
1. 43
2. 48
3. 91
4. 53
Show answer

Answer: (A) 43

Explanation: Each remainder is 5 less than its divisor. Hence the number is LCM(12, 16, 24) − 5 = 48 − 5 = 43.
A school has 216 pencils and 288 erasers. It makes the maximum number of identical gift packets using everything. How many items are in each packet?
1. 6
2. 72
3. 7
4. 8
Show answer

Answer: (C) 7

Explanation: Maximum packets = HCF(216, 288) = 72. Each contains 216 ÷ 72 + 288 ÷ 72 = 7 items.
Three bells ring every 14, 21 and 35 seconds. They ring together now. How many simultaneous ringings occur in the next 35 minutes, excluding now but including the endpoint?
1. 9
2. 11
3. 10
4. 15
Show answer

Answer: (C) 10

Explanation: They ring together every LCM(14, 21, 35) = 210 seconds. Excluding the initial ringing, the count is 35 × 60 ÷ 210 = 10.
Find the least positive integer that leaves remainder 3 when divided by 8, 12 and 20, and is divisible by 7.
1. 363
2. 843
3. 123
4. 483
Show answer

Answer: (D) 483

Explanation: The number is 120k + 3. Modulo 7 this is k + 3, so the least suitable k is 4 and the number is 483.
If a = 2^5 × 3² × 7 and b = 2³ × 3^4 × 5, find LCM(a, b) ÷ HCF(a, b).
1. 1260
2. 315
3. 630
4. 2520
Show answer

Answer: (A) 1260

Explanation: Cancel the common lowest powers. The ratio is 2² × 3² × 5 × 7 = 1260.
A largest possible divisor d leaves the same remainder r on dividing 613, 853 and 1213. Find d + r.
1. 120
2. 107
3. 133
4. 253
Show answer

Answer: (C) 133

Explanation: d = HCF(240, 360) = 120. Since 613 = 120 × 5 + 13, d + r = 120 + 13 = 133.
Three traffic signals change every 40, 56 and 70 seconds. They change together at 9:10:00 a.m. At what time do they next change together?
1. 9:19:20
2. 9:12:20
3. 9:14:00
4. 9:14:40
Show answer

Answer: (D) 9:14:40

Explanation: LCM(40, 56, 70) = 280 seconds = 4 minutes 40 seconds. Add this to 9:10:00 to get 9:14:40.
What is the least non-negative integer to add to 754 to make it divisible by both 18 and 24?
1. 38
2. 34
3. 72
4. 14
Show answer

Answer: (A) 38

Explanation: LCM(18, 24) = 72, and 754 leaves remainder 34. Add 72 − 34 = 38.
A shop has 378 kg rice, 462 kg wheat and 630 kg maize. Each grain is packed separately in bags of the same maximum capacity, with nothing left. How many bags are needed in total?
1. 70
2. 35
3. 30
4. 42
Show answer

Answer: (B) 35

Explanation: Maximum capacity = HCF(378, 462, 630) = 42 kg. Total bags = (378 + 462 + 630) ÷ 42 = 35.
What is the least non-negative integer to subtract from 9876 so that the result is divisible by 14, 21 and 30?
1. 6
2. 66
3. 126
4. 204
Show answer

Answer: (A) 6

Explanation: LCM(14, 21, 30) = 210. Since 9876 = 210 × 47 + 6, subtract 6.
A rectangular floor measures 6.72 m by 4.80 m. What is the minimum number of equal square tiles needed to cover it without cutting?
1. 48
2. 35
3. 70
4. 96
Show answer

Answer: (B) 35

Explanation: Largest tile side = HCF(672, 480) = 96 cm. Minimum tiles = (672 ÷ 96) × (480 ÷ 96) = 35.
Find the HCF of 168, 252 and 420.
1. 126
2. 28
3. 84
4. 42
Show answer

Answer: (C) 84

Explanation: HCF(168, 252) = 84, and 420 = 84 × 5. Hence the required HCF is 84.
The greatest divisor of 1099, 1440 and 1788 leaving remainders 11, 12 and 20 respectively is d. Find d − 20.
1. 48
2. 88
3. 68
4. 34
Show answer

Answer: (A) 48

Explanation: d = HCF(1088, 1428, 1768) = 68. Therefore d − 20 = 48.
What is the smallest four-digit integer divisible by 16, 20 and 28?
1. 1008
2. 1120
3. 1040
4. 1680
Show answer

Answer: (B) 1120

Explanation: LCM(16, 20, 28) = 560. The first multiple at least 1000 is 560 × 2 = 1120.
What is the LCM of 5/12, 7/18 and 11/24?
1. 385/72
2. 1/72
3. 35/6
4. 385/6
Show answer

Answer: (D) 385/6

Explanation: For reduced fractions, LCM = LCM of numerators ÷ HCF of denominators = 385/6.
The ratio of two positive integers is 6:10 and their LCM exceeds their HCF by 308. Find the smaller integer.
1. 110
2. 33
3. 66
4. 132
Show answer

Answer: (C) 66

Explanation: Reduce the ratio to 3:5. If the HCF is h, then 15h − h = 308, giving h = 22 and the smaller number 3 × 22 = 66.
What is the LCM of 28, 42 and 70?
1. 840
2. 420
3. 210
4. 140
Show answer

Answer: (B) 420

Explanation: Take the highest prime powers: 2² × 3 × 5 × 7 = 420.
Find the greatest integer that divides 879 and 1246 leaving remainders 9 and 16 respectively.
1. 15
2. 60
3. 10
4. 30
Show answer

Answer: (D) 30

Explanation: The divisor must divide 879 − 9 = 870 and 1246 − 16 = 1230. Their HCF is 30.
Two numbers are in the ratio 7:9 and their HCF is 16. What is their sum?
1. 144
2. 256
3. 112
4. 1008
Show answer

Answer: (B) 256

Explanation: Since 7 and 9 are co-prime, the numbers are 16 × 7 and 16 × 9. Their sum is 16 × 16 = 256.
Find the HCF of 0.84, 1.26 and 2.10.
1. 0.042
2. 0.21
3. 4.2
4. 0.42
Show answer

Answer: (D) 0.42

Explanation: HCF(84, 126, 210) = 42. Restore two decimal places to get 0.42.
The ratio of two numbers is 5:8 and their LCM is 680. Find their difference.
1. 136
2. 17
3. 51
4. 85
Show answer

Answer: (C) 51

Explanation: Write the numbers as 5x and 8x. Then 40x = 680, so their difference is 3 × 17 = 51.
Find the least integer greater than 20 that leaves remainder 4 when divided by 6, 10 and 15.
1. 26
2. 30
3. 64
4. 34
Show answer

Answer: (D) 34

Explanation: Such numbers are 30k + 4 because LCM(6, 10, 15) = 30. The first above 20 is 34.

Why it matters

Why HCF and LCM of Numbers MCQ – Part 1 is worth the hours

Where the marks actually come from.

HCF and LCM of Numbers MCQ – Part 1 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 1 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.

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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.

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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.

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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 1

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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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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Questions

HCF and LCM of Numbers MCQ – Part 1 - common questions

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How long is the HCF and LCM of Numbers MCQ – Part 1 quiz?

HCF and LCM of Numbers MCQ – Part 1 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 1 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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