Question

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

Answer 1

No.

Explanation:

When two numbers have `18` as their HCF this means for both of them that they can be written in the form `18a` and `18b` where `a` and `b` are the other factors of the two numbers.

The LCM of these same two numbers can be expressed as `c(18a) = d(18b) = 380` . Now since `a`, `b`, `c`, and `d` should be integers `380/18` should be as well since `ac` or `bd` are integers.

`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.