The highest common factor (HCF) of 18 and 45 is 9, while the least common multiple (LCM) is 90.
Explanation:
To find the HCF, we can list the factors of both numbers:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 45: 1, 3, 5, 9, 15, 45
The common factors of 18 and 45 are 1, 3, and 9. The highest of these is 9, so the HCF is 9.
Next, we find the LCM by using the relationship between HCF and LCM, which states that:
HCF × LCM = (Product of the numbers)
Plugging in our numbers, we have:
9 × LCM = 18 × 45
This simplifies to:
9 × LCM = 810
The LCM is therefore:
LCM = 810 / 9 = 90
So, the final results are: HCF = 9 and LCM = 90.