In this worksheet, we will be finding the lowest common multiple (LCM) and the highest common factor (HCF) of two numbers using their products of prime factors.

__Reminder__

This is how we write 1800 as the product of prime factors: 1800 = 2 |
2 | 1 | 8 | 0 | 0 | |||

2 | 9 | 0 | 0 | |||||

2 | 4 | 5 | 0 | |||||

3 | 2 | 2 | 5 | |||||

3 | 7 | 5 | ||||||

5 | 2 | 5 | ||||||

5 |

In a similar way, we find that 2100 = 2^{2} × 3 × 5^{2} × 7

**Example**

Find the LCM and HCF of 1800 and 2100.

We can put all the prime factors in a Venn Diagram such as this:

To find the HCF, we multiply together the numbers in the intersection.

**HCF **= 2 × 2 × 5 × 5 × 3 = **300**

To find the LCM, we multiply all the numbers in the Venn Diagram

**LCM **= 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7 = 1800 × 7 = **12600**