Short Trick to find LCM using Prime Factorization

Duration: 13 min

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Inside: a video lesson and guided study material.

Module outline

  1. Aptitude: 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, Powers and Exponents (Surds and Indices), Algebra, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, TCS NQT Advanced Quantitative Ability, Speed Mathematics and Basic Mathematics, Arithmetic, Statistics, Partnership, Age Problems, Mental Ability, Mensuration and Geometry, Linear Algebra, Calculus, Trigonometry, Vectors, Gamified / Game Based Aptitude
  2. Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, TCS NQT Advanced Reasoning Ability, Ranking, Order and Sequence, Analogy, Inequality, Data Arrangement, Venn Diagram, Logical Sequence Of Words, Selection Decision Table (Decision Making), Cubes & Dices, Clock, Calendar, Puzzle Solving (Puzzles), Analytical Reasoning (Counting Figures Reasoning), Directions (Direction Test), Blood Relations, Seating Arrangements
  3. Verbal Ability (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Articles, Direct and Indirect Speech, Conjunction, Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Verb
  4. Mega Test:
  5. Grand Test:
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.

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