Highest Common Factor (HCF): The Highest Common Factor (HCF) of two or more numbers is the largest number that divides each of them without leaving a remainder. It is also known as the Greatest Common Divisor (GCD). The HCF of two numbers is the largest number that can divide both numbers evenly. For example, the HCF of 12 and 18 is 6, as 6 is the largest number that can divide both 12 and 18. The HCF is used in simplifying fractions and in many mathematical calculations. Least Common Multiple (LCM): The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers. The LCM of two numbers is the smallest number that is divisible by both numbers. For example, the LCM of 4 and 6 is 12, as 12 is the smallest number that is divisible by both 4 and 6. The LCM is used in adding and subtracting fractions, as well as in solving equations involving multiple numbers. Relation between HCF and LCM: The relationship between the HCF and LCM of two numbers can be expressed by the formula: HCF x LCM = Product of the two numbers. This formula shows that the product of the HCF and LCM of two numbers is equal to the product of the two numbers themselves. For example, if the HCF of 8 and 12 is 4 and their LCM is 24, then 4 x 24 = 8 x 12. This relationship is fundamental in number theory and helps in solving various mathematical problems efficiently. Understanding the concepts of HCF and LCM is crucial in mathematics, as they are used in various calculations and problem-solving techniques. By knowing how to calculate and apply HCF and LCM, one can simplify complex mathematical operations and equations effectively.

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Hcf and lcm

Highest Common Factor (HCF):
The Highest Common Factor (HCF) of two or more numbers is the largest number that divides each of them without leaving a remainder. It is also known as the Greatest Common Divisor (GCD).

The HCF of two numbers is the largest number that can divide both numbers evenly.
For example, the HCF of 12 and 18 is 6, as 6 is the largest number that can divide both 12 and 18.
The HCF is used in simplifying fractions and in many mathematical calculations.

Least Common Multiple (LCM):
The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers.

The LCM of two numbers is the smallest number that is divisible by both numbers.
For example, the LCM of 4 and 6 is 12, as 12 is the smallest number that is divisible by both 4 and 6.
The LCM is used in adding and subtracting fractions, as well as in solving equations involving multiple numbers.

Relation between HCF and LCM:
The relationship between the HCF and LCM of two numbers can be expressed by the formula: HCF x LCM = Product of the two numbers.

This formula shows that the product of the HCF and LCM of two numbers is equal to the product of the two numbers themselves.
For example, if the HCF of 8 and 12 is 4 and their LCM is 24, then 4 x 24 = 8 x 12.
This relationship is fundamental in number theory and helps in solving various mathematical problems efficiently.

Understanding the concepts of HCF and LCM is crucial in mathematics, as they are used in various calculations and problem-solving techniques. By knowing how to calculate and apply HCF and LCM, one can simplify complex mathematical operations and equations effectively.

Answered by Praveen Kumar · View profile

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