HCF and LCM Basics

Think of HCF (Highest Common Factor) as finding the biggest number that can divide evenly into two or more numbers. For instance, if you've got 30 and 40, their HCF is 10 because that's the largest number that goes into both without leaving remainders.

LCM (Lowest Common Multiple) works the opposite way - it's the smallest number that both your original numbers can multiply into. Using 20 and 30 as examples, their LCM is 60 because that's the smallest number that both 20 and 30 divide into evenly.

The clever trick is using Venn diagrams with prime factorisation. First, break down your numbers into their prime factors $like 20 = 5 × 2 × 2$. Then pop these factors into a Venn diagram, putting shared factors in the middle overlap.

Quick Tip: For HCF, multiply only the numbers in the middle section. For LCM, multiply absolutely everything in the entire diagram!

For the HCF, you only multiply the shared factors in the middle. For the LCM, you multiply every single number across the whole Venn diagram. It's like the difference between finding what's common versus finding what covers everything!