MathematicsChapter 4: Factorization and Algebraic Manipulation
Hcf and Lcm
HCF of 6 x^2 y and 9 x y^2 is 3 x y.
Learning objectives
- Define and explain hcf and lcm.
- Apply hcf and lcm to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
HCF of 6 x^2 y and 9 x y^2 is 3 x y. LCM is 18 x^2 y^2. For quadratics, factor, then pick common brackets for HCF and all brackets for LCM.
Where / symbols
- Hcf And Lcm
- HCF of 6 x^2 y and 9 x y^2 is 3 x y. LCM is 18 x^2 y^2. For quadratics, factor, then pick common brackets for HCF and all brackets for LCM.
Overview
Learn the idea, then use it:
Core Understanding
HCF of 6 x^2 y and 9 x y^2 is 3 x y. LCM is 18 x^2 y^2. For quadratics, factor, then pick common brackets for HCF and all brackets for LCM.
Examples common lowest · all highest · factorise first · HCF AND LCM: HCF of 6 x^2 y and 9 x y^2 is 3 x y. LCM is 18 x^2 y^2. For quadratics, factor, then pick common brackets for HCF and al
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — HCF AND LCM
HCF of 6 x^2 y and 9 x y^2 is 3 x y. LCM is 18 x^2 y^2. For quadratics, factor, then pick common brackets for HCF and all brackets for LCM.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge hcf and lcm with a neighbouring idea that uses a different definition, rule, or method.
Key points
- common lowest
- all highest
- factorise first
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Hcf and Lcm
Sticky Notes · Quick Revision
Core Idea
- HCF of 6 x^2 y and 9 x y^2 is 3 x y.
Key Points
- common lowest
- all highest
- factorise first
Simple Check
- Explain hcf and lcm in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge hcf and lcm with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- HCF of 6 x^2 y and 9 x y^2 is 3 x y.
- common lowest
- all highest
- factorise first
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