The topics of HCF (Highest Common Factor) and LCM (Lowest Common Multiple) form the foundation of several arithmetic concepts and are a consistent part of the <a href="https://Staff Selection Commission Combined Graduate Level (SSC CGL)">Staff Selection Commission Combined Graduate Level (SSC CGL)</a> exam pattern. Every year, 1–2 questions based on these topics appear across almost every shift of the Tier-I examination, making them highly relevant from a scoring perspective. These chapters and SSC CGL HCF and LCM important questions are not only formula-driven but also test a candidate’s ability to apply logic and numerical relationships quickly and accurately. As such, aspirants are expected to be well-versed in prime factorization, number properties, and reverse calculation methods to effectively handle the varying question formats. In this blog, we focus exclusively on SSC CGL HCF and LCM important questions curated from previous year papers, mock test patterns, and expected exam formats. Whether it’s a straightforward calculation, a real-life word problem, or a complex successive division model, each question here is designed to enhance your practical understanding and <a href="https://ssc.gov.in/home/notice-board">SSC CGL 2025</a> exam-readiness. These questions, along with detailed solutions and shortcut techniques, are structured to help you save time in the exam while maintaining accuracy. If you’ve already read our previous blog, <a href="https://www.quantsir.com/miscellaneous/ssc-cgl-lcm-and-hcf-weightage-and-importance">SSC CGL HCF and LCM</a>, this practice-focused continuation will give you the edge you need. <img loading="lazy" alt="SSC CGL HCF and LCM Important Questions" src="https://www.quantsir.com/admin/assets/uploads/ckeditor/SSC_CGL_HCF_and_LCM_Important_Questions.webp" style="height:338px; width:600px"> [Source: Quant Sir] <h2 id="content-id-131255-0">SSC CGL HCF and LCM Important Questions - Basic Questions</h2> To begin solving SSC CGL HCF and LCM important questions, it’s essential to master direct applications of formulas and number properties. These types are generally asked in every Tier-I paper. Q1. Find the HCF and LCM of 288, 432, and 768. Solution: Prime factorizations: 288 = 25 × 32 432 = 24 × 33 768 = 28 × 3 HCF = 24 × 3 = 48 LCM = 28 × 33 = 6912 Q2. The product of two numbers is 2520, and their HCF is 6. What is their LCM? Solution: Using the identity: Product = HCF × LCM → LCM = 2520 / 6 = 420 Q3. If the HCF of two numbers is 12, which of the following can never be their LCM: 60, 72, 80, 84? Solution: → LCM must be a multiple of 12. Only 80 is not divisible by 12 Answer: 80 These direct concept-based SSC CGL HCF and LCM important questions are quick to solve and help boost your confidence early in the exam. <h2 id="content-id-131255-1">SSC CGL HCF and LCM Important Questions - Word Problems on LCM</h2> This category of SSC CGL HCF and LCM important questions includes real-life scenarios, such as bells tolling or cycles repeating, typically solved using LCM logic. Q1. Six bells toll at intervals of 2, 4, 6, 8, 10, and 12 seconds. When will they toll together again? Solution: → LCM of 2, 4, 6, 8, 10, 12 = 120 seconds Q2. Mahesh distributes marbles among 8, 12, and 18 kids, leaving 5 marbles each time. Total marbles < 200. Find the number of marbles. Solution: Required form: LCM(8,12,18) + 5 = 72k + 5 Try k = 1 or 2 Answer: 77 or 149 Q3. Find the least number which, when divided by 4, 11, and 13, leaves a remainder of 1 in each case. Solution: → LCM(4, 11, 13) + 1 = 572 + 1 = 573 These word-based SSC CGL HCF and LCM important questions test real-time application and demand quick LCM calculation or reasoning. <h2 id="content-id-131255-2">SSC CGL HCF and LCM Important Questions - HCF Through Long Division & Difference Method</h2> Among all SSC CGL HCF and LCM important questions, this type focuses on identifying HCF using subtraction or successive division, ideal for quick solutions. Q1. Find the HCF of 1363 and 1457 using long division. Solution: 1457 ÷ 1363 = Remainder = 94 1363 ÷ 94 = Remainder = 49 94 ÷ 49 = Remainder = 45 49 ÷ 45 = Remainder = 4 45 ÷ 4 = Remainder = 1 4 ÷ 1 = 0 → HCF = 1 Q2. Find the HCF of 2704, 2700, 1586 using the difference method. Solution: Min difference = 2704 – 2700 = 4 → HCF = 2 Q3. Find the HCF of 156 and 140. Solution: Difference = 16 → Highest common factor of 16 that divides both = 4 The SSC CGL HCF and LCM important questions based on the long division or difference method can be solved in under a minute with a smart application. <h2 id="content-id-131255-3">SSC CGL HCF and LCM Important Questions - Successive Division & Mixed Remainder-Based Models</h2> Some of the trickiest SSC CGL HCF and LCM important questions involve layered remainder logic and require a step-wise reverse solving approach. Q1. A number when divided by 5, 6, and 8 successively leaves remainders 1, 3, and 4. Find the remainder when the largest 3-digit number is divided by 9. Solution: → Base number: (((4 × 6) + 3) × 5) + 1 = 136 Largest 3-digit form: 136 + 240 × 3 = 856 → 856 ÷ 9 → Remainder = 1 Q2. Find the smallest number which, when divided by 6, 4, and 2 successively, leaves remainders 4, 2, and 1. Solution: Reverse construction gives: (((1 × 4) + 2) × 6) + 4 = 40 SSC CGL HCF and LCM important questions based on successive division appear complex, but model-based solving ensures speed and accuracy. <h2 id="content-id-131255-4">SSC CGL HCF and LCM Important Questions - Fractions and Properties Based HCF and LCM</h2> Advanced SSC CGL HCF and LCM important questions may feature fractions or constraints, testing your ability to break down numerators and denominators smartly. Q1. Find LCM of 3/7, 5/9, 4/10, and 8/9. Solution: Convert 4/10 → 2/5 LCM = LCM of numerators / HCF of denominators = LCM(3,5,2,8) / HCF(7,9,5,9) → 120 / 1 = 120 Q2. What is the largest number that divides 444, 804, and 1344, leaving the same remainder? Solution: HCF(804–444, 1344–804) → HCF(360, 540) = 180 Q3. A and B are prime numbers such that A > B and LCM is 209. Find B2 – A. Solution:→ 209 = 11 × 19 → A = 19, B = 11 → B2 – A = 121 – 19 = 102 Even twisted or fractional SSC CGL HCF and LCM important questions can be tackled smartly using the right formula-based approach. Mastering SSC CGL HCF and LCM important questions is a strategic advantage for every SSC aspirant aiming to score high in the Quantitative Aptitude section. These questions are not just formula-based but also rely on pattern recognition and logical simplification. With the expert guidance of <a href="https://Quant Sir">Quant Sir</a>, learning these concepts becomes intuitive and time-efficient. Our tricks, short methods, and exam-oriented teaching style help you tackle even the most twisted problems with confidence. <a href="https://www.quantsir.com/topic-wise-test">Practice</a> regularly, focus on speed and accuracy, and let QuantSir’s approach guide your preparation to success in SSC CGL. Stay tuned to level up your preparation with our exclusive smart hacks.

The topics of HCF (Highest Common Factor) and LCM (Lowest Common Multiple) form the foundation of several arithmetic concepts and are a consistent part of the <a href="https://Staff Selection Commission Combined Graduate Level (SSC CGL)">Staff Selection Commission Combined Graduate Level (SSC CGL)</a> exam pattern. Every year, 1&ndash;2 questions based on these topics appear across almost every shift of the Tier-I examination, making them highly relevant from a scoring perspective. These chapters and SSC CGL HCF and LCM important questions are not only formula-driven but also test a candidate&rsquo;s ability to apply logic and numerical relationships quickly and accurately. As such, aspirants are expected to be well-versed in prime factorization, number properties, and reverse calculation methods to effectively handle the varying question formats.

In this blog, we focus exclusively on SSC CGL HCF and LCM important questions curated from previous year papers, mock test patterns, and expected exam formats. Whether it&rsquo;s a straightforward calculation, a real-life word problem, or a complex successive division model, each question here is designed to enhance your practical understanding and <a href="https://ssc.gov.in/home/notice-board">SSC CGL 2025</a> exam-readiness. These questions, along with detailed solutions and shortcut techniques, are structured to help you save time in the exam while maintaining accuracy. If you&rsquo;ve already read our previous blog, <a href="https://www.quantsir.com/miscellaneous/ssc-cgl-lcm-and-hcf-weightage-and-importance">SSC CGL HCF and LCM</a>, this practice-focused continuation will give you the edge you need.

<img loading="lazy" alt="SSC CGL HCF and LCM Important Questions" src="https://www.quantsir.com/admin/assets/uploads/ckeditor/SSC_CGL_HCF_and_LCM_Important_Questions.webp" style="height:338px; width:600px" />

[Source: Quant Sir]

<h2>SSC CGL HCF and LCM Important Questions - Basic Questions</h2>

To begin solving SSC CGL HCF and LCM important questions, it&rsquo;s essential to master direct applications of formulas and number properties. These types are generally asked in every Tier-I paper.

Q1. Find the HCF and LCM of 288, 432, and 768.

Solution: Prime factorizations:

288 = 25 &times; 32

432 = 24 &times; 33

768 = 28 &times; 3

HCF = 24 &times; 3 = 48

LCM = 28 &times; 33 = 6912

Q2. The product of two numbers is 2520, and their HCF is 6. What is their LCM?

Solution: Using the identity: Product = HCF &times; LCM

&rarr; LCM = 2520 / 6 = 420

Q3. If the HCF of two numbers is 12, which of the following can never be their LCM: 60, 72, 80, 84?

Solution: &rarr; LCM must be a multiple of 12. Only 80 is not divisible by 12

Answer: 80

These direct concept-based SSC CGL HCF and LCM important questions are quick to solve and help boost your confidence early in the exam.

<h2>SSC CGL HCF and LCM Important Questions - Word Problems on LCM</h2>

This category of SSC CGL HCF and LCM important questions includes real-life scenarios, such as bells tolling or cycles repeating, typically solved using LCM logic.

Q1. Six bells toll at intervals of 2, 4, 6, 8, 10, and 12 seconds. When will they toll together again?

Solution: &rarr; LCM of 2, 4, 6, 8, 10, 12 = 120 seconds

Q2. Mahesh distributes marbles among 8, 12, and 18 kids, leaving 5 marbles each time. Total marbles &lt; 200. Find the number of marbles.

Solution: Required form: LCM(8,12,18) + 5 = 72k + 5

Try k = 1 or 2

Answer: 77 or 149

Q3. Find the least number which, when divided by 4, 11, and 13, leaves a remainder of 1 in each case.

Solution: &rarr; LCM(4, 11, 13) + 1 = 572 + 1 = 573

These word-based SSC CGL HCF and LCM important questions test real-time application and demand quick LCM calculation or reasoning.

<h2>SSC CGL HCF and LCM Important Questions - HCF Through Long Division &amp; Difference Method</h2>

Among all SSC CGL HCF and LCM important questions, this type focuses on identifying HCF using subtraction or successive division, ideal for quick solutions.

Q1. Find the HCF of 1363 and 1457 using long division.

Solution: 1457 &divide; 1363 = Remainder = 94

1363 &divide; 94 = Remainder = 49

94 &divide; 49 = Remainder = 45

49 &divide; 45 = Remainder = 4

45 &divide; 4 = Remainder = 1

4 &divide; 1 = 0

&rarr; HCF = 1

Q2. Find the HCF of 2704, 2700, 1586 using the difference method.

Solution: Min difference = 2704 &ndash; 2700 = 4

&rarr; HCF = 2

Q3. Find the HCF of 156 and 140.

Solution: Difference = 16

&rarr; Highest common factor of 16 that divides both = 4

The SSC CGL HCF and LCM important questions based on the long division or difference method can be solved in under a minute with a smart application.

<h2>SSC CGL HCF and LCM Important Questions - Successive Division &amp; Mixed Remainder-Based Models</h2>

Some of the trickiest SSC CGL HCF and LCM important questions involve layered remainder logic and require a step-wise reverse solving approach.

Q1. A number when divided by 5, 6, and 8 successively leaves remainders 1, 3, and 4. Find the remainder when the largest 3-digit number is divided by 9.

Solution: &rarr; Base number: (((4 &times; 6) + 3) &times; 5) + 1 = 136

Largest 3-digit form: 136 + 240 &times; 3 = 856

&rarr; 856 &divide; 9 &rarr; Remainder = 1

Q2. Find the smallest number which, when divided by 6, 4, and 2 successively, leaves remainders 4, 2, and 1.

Solution: Reverse construction gives: (((1 &times; 4) + 2) &times; 6) + 4 = 40

SSC CGL HCF and LCM important questions based on successive division appear complex, but model-based solving ensures speed and accuracy.

<h2>SSC CGL HCF and LCM Important Questions - Fractions and Properties Based HCF and LCM</h2>

Advanced SSC CGL HCF and LCM important questions may feature fractions or constraints, testing your ability to break down numerators and denominators smartly.

Q1. Find LCM of 3/7, 5/9, 4/10, and 8/9.

Solution: Convert 4/10 &rarr; 2/5

LCM = LCM of numerators / HCF of denominators = LCM(3,5,2,8) / HCF(7,9,5,9)

&rarr; 120 / 1 = 120

Q2. What is the largest number that divides 444, 804, and 1344, leaving the same remainder?

Solution: HCF(804&ndash;444, 1344&ndash;804)

&rarr; HCF(360, 540) = 180

Q3. A and B are prime numbers such that A &gt; B and LCM is 209. Find B2 &ndash; A.

Solution:&rarr; 209 = 11 &times; 19 &rarr; A = 19, B = 11

&rarr; B2 &ndash; A = 121 &ndash; 19 = 102

Even twisted or fractional SSC CGL HCF and LCM important questions can be tackled smartly using the right formula-based approach.

Mastering SSC CGL HCF and LCM important questions is a strategic advantage for every SSC aspirant aiming to score high in the Quantitative Aptitude section. These questions are not just formula-based but also rely on pattern recognition and logical simplification. With the expert guidance of <a href="https://Quant Sir">Quant Sir</a>, learning these concepts becomes intuitive and time-efficient. Our tricks, short methods, and exam-oriented teaching style help you tackle even the most twisted problems with confidence. <a href="https://www.quantsir.com/topic-wise-test">Practice</a> regularly, focus on speed and accuracy, and let QuantSir&rsquo;s approach guide your preparation to success in SSC CGL. Stay tuned to level up your preparation with our exclusive smart hacks.

SSC CGL HCF and LCM Important Questions - Weightage

SSC CGL HCF and LCM Important Questions - Weightage

SSC CGL LCM and HCF - Weightage and Importance

SSC CGL Number System Important Questions - Weightage

Click to get the infographics of the SSC CGL HCF and LCM Important Questions for the different questions that can be asked, along with their weightage.

SSC CGL HCF and LCM Important Questions - Basic Questions

SSC CGL HCF and LCM Important Questions - Word Problems on LCM

SSC CGL HCF and LCM Important Questions - HCF Through Long Division & Difference Method

SSC CGL HCF and LCM Important Questions - Successive Division & Mixed Remainder-Based Models

SSC CGL HCF and LCM Important Questions - Fractions and Properties Based HCF and LCM

SSC CGL HCF and LCM Important Questions - Weightage

SSC CGL HCF and LCM Important Questions FAQs

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