Short Trick to find LCM using Co-Prime Numbers Concept

Duration: 9 min

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AI Summary

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This educational video, presented by Yash Jain from Knowledge Gate Eduventures, provides a comprehensive lesson on finding the Least Common Multiple (LCM) using the concept of co-prime numbers. The lecture begins with an introduction to the topic, followed by a clear definition of co-prime numbers, stating that any two consecutive numbers (e.g., 12 and 13) and any two prime numbers are co-prime. The core principle is established: the LCM of two co-prime numbers is simply their product. The video then demonstrates this rule through a series of worked examples. The first example, LCM(7, 10, 13), shows that since these numbers are co-prime, their LCM is 7 × 10 × 13 = 910. The second example, LCM(12, 18), illustrates a different method: first, the Highest Common Factor (HCF) is found to be 6, and the numbers are divided by it to get a co-prime pair (2, 3). The LCM is then calculated as HCF × (co-prime pair product) = 6 × 6 = 36. The final example, LCM(48, 72), reinforces the method by showing the HCF is 24, leading to a co-prime pair (2, 3), and the LCM is 24 × 6 = 144. The video concludes with a thank you message.

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 classroom setting with a cartoon teacher and a live instructor, Yash Jain. The main topic is introduced as 'Least Common Multiple (LCM)' on a green chalkboard. The instructor, visible in a small window, begins the lesson by explaining the concept of LCM and HCF, setting the stage for a detailed explanation of a shortcut method.

  2. 2:00 – 5:00 02:00-05:00

    The video focuses on a slide titled '5. LCM using Co-prime Numbers'. The instructor explains that any two consecutive numbers (e.g., 12 and 13) and any two prime numbers are co-prime. The key rule is highlighted: 'Product of two co-prime numbers = LCM'. The instructor emphasizes that when numbers have no common factor, their LCM is their product. This concept is demonstrated with the example LCM(7, 10, 13), where the numbers are shown to be co-prime, and the LCM is calculated as 7 × 10 × 13 = 910.

  3. 5:00 – 8:47 05:00-08:47

    The instructor presents a second method for finding LCM using co-prime numbers. The example LCM(12, 18) is used. The HCF of 12 and 18 is found to be 6. The numbers are divided by the HCF to get a co-prime pair (2, 3). The LCM is then calculated as HCF × (product of co-prime pair) = 6 × 6 = 36. This method is reinforced with a third example, LCM(48, 72), where the HCF is 24, leading to a co-prime pair (2, 3), and the LCM is 24 × 6 = 144. The video concludes with a 'THANKS FOR WATCHING' screen.

The video presents a clear, step-by-step progression on a specific mathematical shortcut. It starts by defining the core concept of co-prime numbers and establishing the fundamental rule that their LCM is their product. This is then applied to a simple case of three co-prime numbers. The lesson then advances to a more complex scenario, demonstrating a two-step method for numbers that are not co-prime: first, find the HCF, then divide the numbers by the HCF to create a co-prime pair, and finally, multiply the HCF by the product of the co-prime pair. This synthesis of the HCF and co-prime concepts provides a powerful and efficient technique for calculating the LCM.