Short Trick to find LCM of 2 numbers when HCF is given

Duration: 6 min

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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate Eduventures, provides a comprehensive lesson on finding the Least Common Multiple (LCM) of two numbers when their Highest Common Factor (HCF) is known. The video begins with an introduction to the topic, followed by a detailed explanation of the fundamental relationship between the product of two numbers, their HCF, and their LCM. This key formula, 'Product of numbers = HCF * LCM', is highlighted as an 'Important Result'. The instructor demonstrates this formula with a worked example using the numbers 12 and 20, showing how to calculate the HCF and then use the formula to find the LCM. The core of the video is a practical application of this formula to solve a specific problem: 'If HCF of 189 and 297 is 27, find their LCM.' The instructor walks through the calculation step-by-step, multiplying the two numbers (189 x 297) and dividing the result by the HCF (27) to arrive at the final answer of 2079. The video concludes with a summary of the method and a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying 'LCM & HCF' against a digital, data-stream background. It then transitions to a lecture screen with a cartoon teacher and a live video feed of the instructor, Yash Jain. The screen shows the topic 'HCF' and 'LCM' with examples of their calculation methods. The instructor introduces the concept of finding the LCM when the HCF is known, setting up the problem: 'If HCF of 189 and 297 is 27, find their LCM.' The on-screen text clearly states the question and the given HCF value.

  2. 2:00 – 5:00 02:00-05:00

    The instructor explains the core formula for solving the problem. He writes on the screen: 'Product of numbers = HCF * LCM'. He then demonstrates this with an example using the numbers 12 and 20, calculating their HCF as 4 and their LCM as 60, and verifying the formula: 12 x 20 = 4 x 60. After establishing this method, he returns to the original problem. He writes the equation: LCM x HCF = 189 x 297. He substitutes the known HCF value of 27, resulting in LCM x 27 = 189 x 297. He then performs the division: LCM = (189 x 297) / 27, which simplifies to LCM = 7 x 297, and finally calculates the result as 2079.

  3. 5:00 – 6:00 05:00-06:00

    The video concludes with a summary of the 'Important Result' formula: 'Product of numbers = HCF * LCM'. The instructor reiterates that this formula is the key to solving such problems efficiently. The final frame is a black screen with an orange and white 'THANKS FOR WATCHING' message, signaling the end of the lesson.

The video presents a clear, step-by-step tutorial on a specific mathematical problem. It effectively uses a combination of visual aids, including on-screen text and handwritten equations, to teach the relationship between HCF and LCM. The instructor first establishes the fundamental formula as a key concept, then applies it to a concrete example to build understanding, and finally uses this knowledge to solve the initial problem. The progression from theory to application provides a solid learning framework for students to solve similar problems.

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