Class 6 Maths - ICSE
HCF and LCM
The chapter on HCF (Highest Common Factor) and LCM (Lowest Common Multiple) is a foundational building block in Class 6 ICSE Mathematics. It helps students understand the relationships between numbers, primes, and composites deeply. You will learn multiple methods to find HCF and LCM, including prime factorization and division method, alongside important word problems that appear frequently in school exams. Mastering this chapter is essential because these concepts are heavily used in higher classes for simplifying fractions, solving ratios, and working with algebraic expressions in upcoming ICSE board curricula.
Start Learning FreeKey Concepts
Factors
A factor of a number is an exact divisor of that number, meaning it divides the number without leaving any remainder.
Multiples
A multiple of a number is obtained by multiplying that number by any whole number, resulting in a product that is greater than or equal to the number itself.
Highest Common Factor (HCF)
HCF, also known as Greatest Common Divisor (GCD), is the largest number that divides two or more given numbers completely without leaving a remainder.
Lowest Common Multiple (LCM)
LCM is the smallest positive number that is a common multiple of two or more given numbers.
Prime Factorization Method
A systematic way of breaking down a composite number into a product of prime numbers to easily calculate both HCF and LCM.
Important Formulas
Board Exam Info
In ICSE Class 6 Mathematics examinations, this chapter typically carries around 6 to 10 marks. Common question types include finding the HCF and LCM of three numbers using prime factorization or division methods, and word problems involving bells ringing together or items distributed in equal rows.
Frequently Asked Questions
Use HCF when the problem asks for maximum, largest, splitting into equal parts, or greatest arrangement. Use LCM when the problem mentions minimum, least, repeating events together, or simultaneous occurrences like bells ringing at the same time.
What is the difference between prime factors and common factors?
Prime factors are the prime numbers that multiply to give a number (like 2 and 3 for 6). Common factors are the numbers that divide two or more given numbers without a remainder.
Can the HCF of two numbers be greater than the numbers themselves?
No, the HCF is always less than or equal to the smallest of the given numbers because a factor cannot be larger than the number it divides.
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