The Highest Common Factor (HCF), also called GCD (Greatest Common Divisor), is the largest number that divides both values without a remainder. It's used to simplify fractions, split things into equal groups, and in cryptography.
The Lowest Common Multiple (LCM) is the smallest number that both values divide into exactly. It's used to find common denominators when adding fractions, and to solve problems involving repeating events ("when will they coincide again?").
What are co-prime numbers?
Two numbers are co-prime (or relatively prime) if their HCF is 1. For example, 7 and 13 share no common factors, so HCF = 1 and LCM = 7 × 13 = 91.
How are HCF and LCM related?
HCF × LCM = A × B. This shortcut means if you know one, you can always find the other.