Understanding LCM and HCF - Simple Guide

Finding LCM and HCF - The Essentials

The lowest common multiple (LCM) is the smallest number that both your original numbers divide into evenly. For simple numbers like 3 and 5, just list out their multiples until you spot a match - in this case, it's 15.

For trickier numbers like 60 and 96, use prime factorisation. Break each number down into its prime factors: 60 = 2 × 2 × 3 × 5 and 96 = 2 × 2 × 2 × 2 × 2 × 3. Then spot the common factors $2 × 2 × 3 = 12$ - this is your highest common factor (HCF).

Here's the clever bit: LCM = HCF × all the leftover factors. So 12 × 5 × 2 × 2 × 2 = 480. This method saves loads of time compared to listing out multiples!

Quick Check: The HCF is what both numbers share in common, while the LCM is the smallest number they both fit into perfectly.