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 = 23 × 32 × 52 |
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 = 22 × 3 × 52 × 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