HCF refers to the greatest common factor of two or more integers, that is, the largest positive integer that can be divisible simultaneously between them. For example, HCF( 12, 18) = 6, because the common factor of 12 and 18 is 1, 2, 3, 6, 6 is the largest.
LCM refers to the least common multiple of two or more integers, that is, the smallest positive integer among the common multiples between them. For example, LCM( 12, 18) = 36, because multiples of 12 are 12, 24 and 36, while multiples of 18 are 18 and 36, 36 is their minimum.
When calculating HCF and LCM, the common method is to decompose the prime factors of these numbers. For example, to calculate HCF( 12, 18), we can decompose them into prime factors: 12 = 2x3x3, 18 = 2 x 3 x 3, and then find out their common factors, that is, 2 and 3. The greatest common factor is 6. Similarly, you can multiply their prime factors and then divide them by their common factors to get their least common multiple.