Topics
Number System(Consolidating the Sense of Numberness)
Number System
Estimation
Ratio and Proportion
Algebra
Numbers in India and International System (With Comparison)
Geometry
Place Value
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Data Handling
Negative Numbers and Integers
Number Line
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
Sets
Ratio
Proportion (Including Word Problems)
Unitary Method
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
Percent (Percentage)
Idea of Speed, Distance and Time
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
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
- Definition: LCM
- Steps to Find the LCM
- Examples
Definition: LCM
The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.
Steps to Find the LCM
Examples
(2 and 5)
- List the multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... - List the multiples of 5:
5, 10, 15, 20, ... - Identify the common multiples:
Common multiples of 2 and 5 include numbers such as 10, 20, and so on. - Choose the smallest common multiple:
The smallest is 10 - Final Answer:
LCM(2, 5) = 10
Note:
The LCM of two numbers cannot be bigger than their product.
Example Question 1
In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?
The distance covered by each one of them is required to be the same as well as a minimum. The required minimum distance each should walk would be the lowest common multiple of the measures of their steps.
Thus, we find the LCM of 80, 85, and 90.
The LCM of 80, 85, and 90 is 12240.
The required minimum distance is 12240 cm.
Example Question 2
Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case.
We first find the LCM of 12, 16, 24, and 36 as follows:
Thus, LCM = 2 × 2 × 2 × 2 × 3 × 3 = 144
144 is the least number which when divided by the given numbers will leave remainder 0 in each case. But we need the least number that leaves remainder 7in each case.
Therefore, the required number is 7 more than 144.
The required least number = 144 + 7 = 151.
Example Question 3
Add: `17/28 + 11/35`
Let us find the LCM of 28 and 35 in order to add the fractions.
LCM = 7 × 4 × 5 = 140
`17/28 + 11/35 = (17 xx 5)/(28 xx 5) + (11 xx 4)/(35 xx 4) = (85 + 44)/140 = 129/140`.
Example Question 4
On dividing a certain number by 8, 10, 12, 14 the remainder is always 3. Which is the smallest such number?
| 2 | 8 | 10 | 12 | 14 |
| 2 | 4 | 5 | 6 | 7 |
| 2 | 5 | 3 | 7 |
Let us find the LCM of the given divisors.
LCM = 2 × 2 × 2 × 5 × 3 × 7 = 840.
To the LCM we add the remainder obtained every time.
Hence, that number = LCM + remainder = 840 + 3 = 843
Example Question 5
Shreyas, Shalaka, and Snehal start running from the same point on a circular track at the same time and complete one lap of the track in 16 minutes, 24 minutes, and 18 minutes respectively. What is the shortest period of time in which they will all reach the starting point together?
The number of minutes they will take to reach together will be a multiple of 16, 24, and 18.
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
18 = 2 × 3 × 3
LCM = 2 × 2 × 2 × 2 × 3 × 3 = 144.
They will come together in 144 minutes or 2 hours 24 minutes.
