# HCF and LCM Questions for Bank Exams | Free Timed Practice > Practise HCF and LCM questions free and timed for IBPS, SBI, SSC and railway prelims. Euclid Source: https://computeprep.com/drill-types/hcf-and-lcm --- Exam path · HCF & LCM ## HCF and LCM questions, solved by one identity HCF and LCM questions test two numbers through one identity: the product of any two numbers equals their HCF multiplied by their LCM. Find the HCF by repeated division — Euclid's algorithm — and the LCM as the product divided by that HCF. When one number and both HCF and LCM are given, the missing number is HCF times LCM, divided by the number you already have. HCF and LCM questions are a fixed, low-variance couple of marks in bank and SSC papers, and the entire topic collapses to one identity: product equals HCF times LCM. Once that relationship is memorised the questions stop being arithmetic to work through and become substitution to check. **Try it against the clock.** HCF & LCM runs at 30s easy, 40s medium and 55s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading. [Start a timed HCF & LCM drill →](https://computeprep.com/?drill=hcf_lcm&src=seo-hcf-and-lcm) ### How to solve HCF and LCM questions with the product identity - Find the HCF by Euclid's algorithm Divide the larger number by the smaller, then keep dividing the divisor by the remainder until the remainder is zero — the last non-zero divisor is the HCF. For 36 and 48: 48 = 1×36 + 12, 36 = 3×12 + 0, so HCF = 12. - Get the LCM from the product, not from listing multiples LCM = (first number × second number) ÷ HCF. For 12 and 18: HCF is 6, product is 216, so LCM = 216 ÷ 6 = 36. - Use the same identity in reverse when a number is missing If HCF and LCM are both given along with one number, the other number = (HCF × LCM) ÷ the known number. This is the same relationship read the other way round. - Check the HCF you found actually divides both original numbers A HCF that doesn't divide one of the two starting numbers exactly means an arithmetic slip happened earlier — this check catches it before you commit to an answer. ### Three shapes of the same question | What the paper asks | The move | | --- | --- | | Find the HCF of two numbers | Euclid's algorithm — divide, then divide the remainder, until it hits zero | | Find the LCM of two numbers | LCM = product ÷ HCF, never list multiples | | One number is missing, HCF and LCM given | Missing number = (HCF × LCM) ÷ the known number | ### 3 real hcf and lcm questions, with worked solutions Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers. #### Question 1 The two numbers are 10 and 21. What is the LCM of 10 and 21? - 420 - 209 - 210 - 211 - 1 - HCF(10, 21) = 1. - LCM = 10 × 21 ÷ 1 = 210. - Answer: 210. #### Question 2 The two numbers are 16 and 20. What is the LCM of 16 and 20? - 80 - 4 - 79 - 16 - 20 - HCF(16, 20) = 4. - LCM = 16 × 20 ÷ 4 = 80. - Answer: 80. #### Question 3 The two numbers are 9 and 18. What is the LCM of 9 and 18? - 18 - 9 - 28 - 17 - 19 - HCF(9, 18) = 9. - LCM = 9 × 18 ÷ 9 = 18. - Answer: 18. ### Common mistakes this drill is built from The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks. #### Listing multiples to find the LCM It works but costs far more time than product ÷ HCF, and under a clock the slower method is the one that leaves a question half-finished, not merely wrong. #### Confusing which answer the question wants HCF and LCM sit on the board together as options for both kinds of question — the LCM is a printed distractor on an HCF question and vice versa. Re-read which one the stem actually asked for before selecting. #### Dividing the LCM by the known number and stopping there That skips the HCF entirely. The identity is product = HCF × LCM, so the missing number is (HCF × LCM) ÷ known, not LCM ÷ known. ### Why your answer came out wrong The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here. #### 36 and 48 — why isn't the HCF 144? 144 is the LCM, not the HCF. Euclid's algorithm gives HCF = 12: 48 = 1×36+12, 36 = 3×12+0. The LCM, 144, is the product 36×48 divided by 12 — it always sits on the board as the near miss when the question asked for the HCF. #### 12 and 18 — why isn't the LCM 6? 6 is the HCF, not the LCM. LCM = product ÷ HCF = (12×18) ÷ 6 = 216 ÷ 6 = 36. The HCF is the smaller number of the two and is the printed near-miss whenever the question actually wants the LCM. #### HCF is 12, LCM is 180, one number is 36 — why isn't the other number 5? 5 comes from dividing the LCM by the known number and stopping — 180 ÷ 36 = 5 — which skips the HCF entirely. The identity is product = HCF × LCM, so the other number is (12 × 180) ÷ 36 = 60. ### FAQ #### What is the fastest method for HCF and LCM questions? Find the HCF with Euclid's algorithm — repeated division until the remainder is zero — then get the LCM as the product of the two numbers divided by that HCF. The same identity, read in reverse, finds a missing number when the HCF and LCM are both given. #### How long should an HCF and LCM question take in prelims? Between 30 and 55 seconds. This drill enforces exactly that: 30 seconds on easy, 40 on medium and 55 on hard, timed on the server rather than in your browser. #### Is there a shortcut instead of Euclid's algorithm for HCF? For small numbers, prime factorising both and taking the common factors at their lowest power is often faster by inspection. Euclid's algorithm is the reliable one for numbers too large to factorise quickly by eye. #### How are HCF and LCM related? For any two numbers, their product always equals their HCF multiplied by their LCM. That single identity is what lets you find the LCM without listing multiples, or find a missing number when the HCF and LCM are both known. ### Practise the next topic - [All 30 drill types](https://computeprep.com/drill-types) — the full rotation with every published time limit. - [Simplification questions — BODMAS](https://computeprep.com/drill-types/simplification) — simplification questions, timed. - [Square root and cube root questions — read the answer off the last digit](https://computeprep.com/drill-types/square-root-cube-root) — square root and cube root questions, timed. - [Ratio and proportion questions](https://computeprep.com/drill-types/ratio-and-proportion) — ratio and proportion questions, timed. - [Vedic maths shortcuts](https://computeprep.com/vedic-maths) — the seven sutras that make a 15-second answer possible. - [How to improve calculation speed](https://computeprep.com/calculation-speed) — the six-week arc these drills fit into. 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