Short Trick to find LCM using Prime Factorization

Duration: 13 min

This video lesson is available to enrolled students.

Return to /learn/DSSSB-TGT-COMPUTER-SCIENCE-COMPLETE-COURSE/arithmetical-numerical-ability/hcf-lcm/finding-lcm/asset-short-trick-to-find-lcm-using-prime-factorization after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lesson on finding the Least Common Multiple (LCM) and Highest Common Factor (HCF) using the prime factorization method. The instructor begins by introducing the topic and then demonstrates the method step-by-step with the example of LCM(12, 18). The process involves breaking down each number into its prime factors, identifying the highest power of each prime factor present in either number, and multiplying these together to find the LCM. The video then applies the same method to find the LCM and HCF of 24 and 60, explicitly showing the prime factorization of 24 as 2^3 x 3 and 60 as 2^2 x 3 x 5. The instructor explains that the LCM is the product of the highest powers of all prime factors (2^3 x 3 x 5 = 120), while the HCF is the product of the lowest powers of the common prime factors (2^2 x 3 = 12). A Venn diagram is used to visually represent this concept, with the intersection representing the HCF and the union representing the LCM. The video concludes by reinforcing the relationship between LCM and HCF with the formula LCM x HCF = product of the two numbers.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for 'LCM & HCF' and transitions to a classroom setting. The instructor, Yash Jain, introduces the topic of 'Least Common Multiple (LCM)' and 'Highest Common Factor (HCF)'. The screen displays a slide with the title '4. LCM using Prime Factorization Method' and the example 'LCM (12, 18)'. The instructor begins to explain the method, setting the stage for a detailed demonstration.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the prime factorization of 12 and 18. He writes the prime factorization of 12 as 2 x 2 x 3, or 2^2 x 3, and for 18 as 2 x 3 x 3, or 2 x 3^2. He then explains the rule for finding the LCM: take the highest power of each prime factor. For 12 and 18, the highest power of 2 is 2^2 and the highest power of 3 is 3^2. He writes the LCM as 2^2 x 3^2, which equals 4 x 9 = 36.

  3. 5:00 – 10:00 05:00-10:00

    The video presents a multiple-choice question: 'The LCM of 2^6 * 3^2 * 5 * 7 and 2^3 * 3^5 * 7 is:'. The instructor explains that to find the LCM, one must take the highest power of each prime factor. The highest power of 2 is 2^6, of 3 is 3^5, of 5 is 5^1, and of 7 is 7^1. He writes the LCM as 2^6 x 3^5 x 5 x 7. The video then moves to a new example, LCM & HCF (24, 60). The instructor writes the prime factorization of 24 as 2^3 x 3 and 60 as 2^2 x 3 x 5.

  4. 10:00 – 13:11 10:00-13:11

    The instructor calculates the LCM of 24 and 60 by taking the highest powers of the prime factors: 2^3, 3^1, and 5^1, resulting in 2^3 x 3 x 5 = 120. He then calculates the HCF by taking the lowest powers of the common prime factors: 2^2 and 3^1, resulting in 2^2 x 3 = 12. A Venn diagram is used to illustrate this, with the intersection (common factors) representing the HCF (2 x 2 x 3 = 12) and the union (all factors) representing the LCM (2 x 2 x 2 x 3 x 5 = 120). The video concludes by showing that LCM x HCF = 120 x 12 = 1440, which equals 24 x 60.

The video systematically teaches the prime factorization method for finding the LCM and HCF. It starts with a clear definition and a simple example (12, 18) to establish the core principle: for LCM, take the highest power of each prime factor; for HCF, take the lowest power of the common prime factors. The lesson progresses to a more complex numerical example (24, 60) and a conceptual multiple-choice question, reinforcing the method. The use of a Venn diagram provides a powerful visual aid to distinguish between the intersection (HCF) and the union (LCM) of the prime factors, making the abstract concept more tangible. The final demonstration of the formula LCM x HCF = product of the numbers serves as a valuable verification step and a key takeaway for students.

Loading lesson…