Class 10Subject Code: 041Year: 202338 Questions Available

CBSE Class 10 Mathematics Standard 2023 — QuizCluster Solutions

Comprehensive question-by-question independently authored solutions for CBSE Class 10 Mathematics Standard Board Examination (2023). Questions are referenced directly to the official CBSE Question Paper.

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Official Source & AttributionSource of question paper: Central Board of Secondary Education (CBSE)

Solutions and conceptual explanations are independently prepared by QuizCluster. QuizCluster is an independent educational platform and is not affiliated with, endorsed by, or sponsored by the Central Board of Secondary Education (CBSE). Official question papers are accessed via direct external links to official CBSE repositories and are never hosted or mirrored on QuizCluster.

Question Index

Q1 of 38

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Fundamental Theorem of Arithmetic (HCF & LCM)

Section A•1 Marks•Chapter: Real Numbers

Easy

Question 1 — Problem Statement (Synopsis)

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If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, find HCF(a, b) and LCM(a, b).

See Question 1 in official CBSE Class 10 Mathematics Standard Question Paper (2023)

QuizCluster Step-by-Step Solution

Step 1: Apply prime power rules for HCF and LCM

Given a = x³ y² and b = x¹ y³ where x, y are primes. HCF(a, b) is the product of smallest powers of common prime factors: HCF = x¹ · y² = x y². LCM(a, b) is the product of greatest powers of all prime factors: LCM = x³ · y³.

Final Answer

HCF(a, b) = x y² | LCM(a, b) = x³ y³

Key Formulas & Mathematical Laws

HCF = Product of smallest powers of common prime factors
LCM = Product of greatest powers of all prime factors
HCF(a, b) × LCM(a, b) = a × b

Important Core Concept

Prime decomposition uniquely identifies greatest common divisors and least common multiples.

Common Student Pitfall

Swapping the minimum and maximum power rules.

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Question 1 of 38

Source of question paper: Central Board of Secondary Education (CBSE). QuizCluster provides independently prepared educational solutions and explanations. QuizCluster is an independent educational platform and is not affiliated with or endorsed by CBSE. Question papers are accessed through links to official CBSE resources and are not hosted by QuizCluster.