Topics
Number System (Including Estimation and Approximation)
Number System
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Ratio and Proportion
Theme 2 : Ratio, Proportion and Arithmetic Problems
Numbers in Indian and International Systems (With Comparison)
Estimation
Theme 3 : Algebra
Numbers in India and International System (With Comparison)
Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Place Value
Negative Numbers and Integers
Geometry
Theme 4 : Geometry
Mensuration
Theme 5 : Mensuration
Sets
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
Theme 6 : Statistics
Data Handling
Fractions
Number Line
Decimal Fractions
Playing with Numbers (Including H.C.F. and L.C.M.)
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Ratio and Proportion (Including Unitary Method)
Sets
Percent (Percentage)
Idea of Speed, Distance and Time
Ratio
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Unitary Method
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Fundamental Concepts (Including Angles and their Properties)
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Triangles (Including Types and Properties of Triangles)
Quadrilaterals
Percent (Percentage)
Circles
Idea of Speed, Distance and Time
Symmetry
Fundamental Concepts
Constructions
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Recognition of Solids
Framing Algebraic Expressions (Including Evaluation)
Perimeter and Area of Plane Figures
Data Handling (Including Mean and Median)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Introduction
- Methods
- Key Points Summary
CISCE: Class 10
Introduction
The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of those numbers.
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To find when two or more repeating cycles match up (e.g., ringing bells, traffic lights).
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To divide things into groups evenly (e.g., arranging students in equal teams).
CISCE: Class 6
Methods
| Method | Steps | Example | Answer (L.C.M.) |
|---|---|---|---|
| Common Multiple Method | 1. List multiples of each number. 2. Find common multiples. 3. Choose the smallest. |
(i) 4, 5, 10 M₄ = 4, 8, 12, 16, 20... M₅ = 5, 10, 15, 20... M₁₀ = 10, 20, 30... Common = 20... |
20 |
| (ii) 12, 15, 20 M₁₂ = 12, 24, 36, 48, 60... M₁₅ = 15, 30, 45, 60... M₂₀ = 20, 40, 60... Common = 60... |
60 | ||
| Prime Factor Method | 1. Write prime factors. 2. Take the highest power of each. 3. Multiply them. |
18 = 2 × 3× 3 = 2¹ × 3² 24 = 2 × 2 × 2 × 3 = 2³ × 3¹ 36 = 2 × 2 × 3 × 3 = 2² × 3² Highest powers = 2³, 3² |
72 |
| L.C.M. = 2³ × 3² = 8 × 9 = 72 | |||
| Common Division Method | 1. Write numbers in a row. 2. Divide by common prime. 3. Repeat till left with coprime numbers. 4. Multiply all divisors & last line. |
16, 20, 24 ÷2 → 8, 10, 12 ÷2 → 4, 5, 6 ÷2 → 2, 5, 3 Then multiply all: 2 × 2 × 2 × 2 × 5 × 3 |
240 |
CISCE: Class 6
Key Points Summary
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LCM is the smallest number divisible by all given numbers.
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Use the listing method for small numbers and the other methods for larger numbers.
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LCM helps solve problems involving cycles and grouping.
