# Can two numbers have 18 as their HCF and 380 as their LCM?

When two numbers have $18$ as their HCF this means for both of them that they can be written in the form $18 a$ and $18 b$ where $a$ and $b$ are the other factors of the two numbers.
The LCM of these same two numbers can be expressed as $c \left(18 a\right) = d \left(18 b\right) = 380$ . Now since $a$, $b$, $c$, and $d$ should be integers $\frac{380}{18}$ should be as well since $a c$ or $b d$ are integers.
$\frac{380}{18} = 21.1111$ which is not an integer. This means that two numbers cannot share 18 as their HCF and 380 as their LCM.