Finding the HCF and LCM of algebraic expressions

Mark Willis

1 Mar 202202:53

Summary

TLDRThis video tutorial explains how to find the highest common factor (HCF) and least common multiple (LCM) of algebraic expressions using prime factorization. The presenter breaks down the components of the expressions 12x²yz² and 15xy²z² into their prime factors, demonstrating the process visually with a Venn diagram. The HCF is identified as 3xy²z², while the LCM is calculated as 60x²y²z². The video emphasizes understanding the concepts of HCF and LCM in the context of algebraic expressions, making it accessible for learners transitioning from numerical to algebraic factors.

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Q & A

What two algebraic expressions are used in the example?
-The two expressions are 12x²yz² and 15xy²z².
How is the prime factorization of 12 performed in the transcript?
-12 is factored into its prime components as 2 × 2 × 3, which can be expressed as 2² × 3.
What method is used to find the HCF and LCM in the video?
-The video uses prime factorization and a Venn diagram to identify common factors for the HCF and to calculate the LCM.
What common factors are found for the expressions 12x²yz² and 15xy²z²?
-The common factors are 3, x, y, and z².
What is the HCF calculated from the given algebraic expressions?
-The HCF is 3xyz².
How is the LCM calculated based on the HCF?
-The LCM is calculated by multiplying the HCF (3xyz²) by the remaining factors not included in the HCF.
What are the additional factors included in the LCM calculation?
-The additional factors are 2² from the first expression and 5 from the second expression.
What is the final result of the LCM for the given expressions?
-The LCM is 60x²y²z².
Why is it important to understand how to find the HCF and LCM of algebraic expressions?
-Understanding how to find the HCF and LCM helps in simplifying algebraic expressions and solving equations involving them.
What does the presenter thank the audience for at the end of the video?
-The presenter thanks the audience for watching and hopes they have understood the process.