All 21 LCM, HCF & Simplification questions the Punjab PSC asked between 2016 and 2026, each with a worked answer and the exam it came from. First 10 free to read.
1 of these 21 were set in more than one exam — the Commission reuses this topic, which is the argument for working through it rather than skimming it.
Free to read, with the worked answer and the exam each one came from. The book prints this topic in the order the Commission favours, so these are the ones to know first.
The bells ring together at every common multiple of their intervals. > LCM(2, 4, 6, 8, 10, 12) = 120 s = 2 min > In 60 min: 60 ÷ 2 = 30 later coincidences > The stem says they commence tolling together, so the start counts: 30 + 1 = 31 So they ring together 31 times in an hour. Rule for PPSC: add the starting toll only when the stem says the bells (or guns) start together; when it does not, count only the coincidences that fall within the hour, as in the five-shooter question (7 times in an hour). Option (b) 30 is the count without the start.
Work the left-hand side first, then move 29.114 across. > 28.314 − 31.427 = −3.113 > −3.113 + 113.928 = 110.815 > ? = 110.815 − 29.114 = 81.701 The missing number is 81.701; option (a) 81.711 is the trap for a slip in the last decimal place.
38 × 56 = 2128 and 2143 − 2128 = 15, so 2143 = 38 × 56 + 15. Quotient = 56, remainder = 15.
√729 = 27 and √7.29 = 2.7. √72.9 = √(729/10) = 27/√10 ≈ 8.538 (note: it is NOT 8.1, since the decimal shifts by √10, not 10). Sum ≈ 27 + 8.538 + 2.7 = 38.238 ≈ 38.23.
Round every part to an easy value. > 13.08 ≈ 13, 24.98 ≈ 25, √624 ≈ 25 > 13 × 25 = 325 > 325 + 25 The answer is about 350.
Simplify from the innermost bracket outwards. Treat ? as x. > 37 − (15 − x) = 22 + x > 28 − (22 + x) = 6 − x > 45 − (6 − x) = 39 + x = 58 → x = 19.
One note of each denomination together is worth 1 + 5 + 10 = ₹16. > Number of each = 480 / 16 = 30 > Total notes = 3 × 30 = 90.
Turn each one into a plain decimal. > a = √0.25 = 0.5 > b = 0.25, c = (0.25)² = 0.0625, d = 0.05 > 0.05 < 0.0625 < 0.25 < 0.5 The order is d < c < b < a.
Work the bottom first. > 3 ÷ (3/2) = 3 × (2/3) = 2 > (2/3) ÷ 2 = 2/6 = 1/3 So the value is 1/3.
The bronze part is 1/5, so 4/5 of the tower remains. A quarter of that is maroon, so the golden part is three-quarters of 4/5. > golden fraction = 3/4 × 4/5 = 3/5 > 3/5 of height = 450 → height = 450 × 5/3 = 750 m So the tower is 750 m tall.
You have read the ten the Commission asks most. The rest of this topic — and all 4,239 questions across the book, each with a worked solution — come with either edition.
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See the printed book →The Commission set 21 LCM, HCF & Simplification questions across 23 papers between 2016–2026. That is the whole set, not a sample — every one of them is in the book, and the 10 most-asked are on this page free.
Yes. 1 of these 21 were set in more than one exam, which is why they are worth working rather than reading. Each question here carries a badge showing how many sittings asked it.
Here. Every question on this page is a solved MCQ: the four options as printed, the correct answer, and a worked explanation in plain English — not just a letter. The rest of the 21 are in the book, in the same form.
Switch to Attempt mode at the top of the questions. You get one question at a time and it is marked the moment you pick an option, with the reason underneath — the same way the exam feels, on your phone.
The questions are on screen rather than in a downloadable file, so they stay current and correct. The printed book has all 21 of these plus the rest of the Reasoning & Aptitude section, and every buyer gets the whole thing online as well.
The exams behind these questions, most first. A paper here is a sitting: a question set in two papers of the same sitting counts once.
| Exam | Year | Questions |
|---|---|---|
| PPSC DDSWO | 2026 | 3 |
| Punjab Civil Services (Prelims) — CSAT | 2025 | 2 |
| Archaeological Chemist(Group-B) | 2025 | 2 |
| Accountants | 2022 | 2 |
| Principal, Industrial Training Institute (Women) | 2024 | 1 |
| Junior Scientific Officer (Group-B) | 2024 | 1 |
| Scientific Assistant (Serology) (Group B) | 2023 | 1 |
| Scientific Officer (Polygraph) (Group B) | 2023 | 1 |
| Scientific Assistant (Biology) (Group B) | 2023 | 1 |
| Scientific Assistant (Polygraph) (Group B) | 2023 | 1 |
| Assistant Town Planner (Group A) | 2023 | 1 |
| Assistant Director Assistant Controller of Stores St | 2022 | 1 |