What is the full form of HCF and LCM?

The full form of HCF is Highest Common Factor, and the full form of LCM is Lowest Common Multiple.

The HCF is the largest number that divides two or more numbers without leaving a remainder, while the LCM is the smallest multiple that is divisible by two or more numbers. Both HCF and LCM are essential in various mathematical operations and problem-solving.

For example, consider the numbers 24 and 36. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The common factors are 1, 2, 3, 4, 6, and 12, with 12 being the greatest among them. Therefore, the HCF of 24 and 36 is 12.

Continuing with the example of 24 and 36, the multiples of 24 are 24, 48, 72, 96, 120, and so on. The multiples of 36 are 36, 72, 108, 144, and so on. The common multiples are 72, 144, and so forth. Among these, 72 is the smallest, making it the LCM of 24 and 36.

In summary, HCF is used to find the largest common factor of two or more numbers, while LCM is used to determine the smallest common multiple. These concepts are fundamental in various mathematical applications, including simplifying fractions, solving equations, and ensuring consistency in measurements and calculations.