What is the difference between LCM and HCF?

Answer 1

LCM (Least Common Multiple) and HCF (Highest Common Factor, also known as GCD or Greatest Common Divisor) are both concepts in mathematics dealing with factors and multiples of numbers, but they serve different purposes:

LCM (Least Common Multiple):

Definition: The smallest positive number that is a multiple of two or more numbers.

Purpose: Used when we need to find the smallest number that is divisible by all the given numbers.

Always greater than or equal to the largest number in the set.

Useful in adding or subtracting fractions with different denominators.

HCF (Highest Common Factor):

Definition: The largest positive integer that divides each of the numbers without a remainder.

Purpose: Used to find the largest number that can divide all the given numbers evenly.

Always less than or equal to the smallest number in the set.

Useful in simplifying fractions and solving certain types of problems involving divisibility.

Key Differences:

LCM is always greater than or equal to the largest number in the set, while HCF is always less than or equal to the smallest number in the set.

LCM is about finding multiples, while HCF is about finding factors.

LCM is used for addition and subtraction of fractions, while HCF is used for simplifying fractions.

The process of finding LCM often involves multiplication, while finding HCF often involves division.

Example:

For numbers 12 and 18:

LCM(12,18) = 36 (the smallest number divisible by both 12 and 18)

HCF(12,18) = 6 (the largest number that divides both 12 and 18 without remainder)

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Answer 2

LCM (Least Common Multiple) and HCF (Highest Common Factor) are two mathematical concepts that are often confused with each other but they are actually opposite in nature.

HCF (Highest Common Factor) also known as (Greatest Common Divisor)

• Finds the largest number that divides two or more numbers exactly without leaving a remainder
• it is the greatest common factor that divides the number
• Example: the HCF of 12 and 15 is 3, because 3 is the largest number that divides both 12 and 15 exactly

LCM (Least Common Multiple)

• Finds the smallest number that is a multiple of two or more numbers
• It is the smallest number that is a common multiple of the numbers.
• Example: LCM of 12 and 15 is 60, because 60 is the smallest number that is a multiple of both 12 and 15

You can watch a tutorial on how to find the HCF and LCM of two or more numbers

youtu.be/DheTDtoRdic

youtu.be/GP3-sWfuYwc