The Highest Common Factor (HCF) and Lowest Common Multiple (LCM) are two important concepts in mathematics often used in solving problems related to fractions, ratios, and proportions. These concepts are used to find the greatest common factor and the smallest common multiple of two or more numbers.

**The Highest Common Factor (HCF) of two or more numbers is the largest number that divides evenly into all of them.** For example, let's find the HCF of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 12 and 18 are 1, 2, 3, and 6. The highest common factor, therefore, is 6. Another example is finding the HCF of 15 and 20. The factors of 15 are 1, 3, 5, and 15, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The common factors of 15 and 20 are 1 and 5. The highest common factor, therefore, is 5.

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