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
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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
