Short Trick to find LCM using Prime Factorization

Duration: 13 min

This video lesson is available to enrolled students.

Return to /learn/RSSB-BASIC-COMPUTER-INSTRUCTOR/paper-1-basic-numeracy/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 the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
  3. Paper-1 & 2 | Data Interpretation: Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Analogy, Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement, Logical Sequence Of Words, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: Selection Decision Table (Decision Making)
  7. Paper-1 | General Science: Physics, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: State Wise GK, GK- Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, Artificial Intelligence
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: Child Development, Theories, Concept of Pedagogy, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Psychology, Curriculum Framework & Reforms, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
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…