Question

Given that the product of two positive integers is 44, and their least common multiple is 22, what is their greatest common divisor?

Answer 1

2

Explanation:

For any positive numbers a,b we always have the following identity:

`a\cdot b=gcd(a,b)\cdot lcm(a,b)`

(gcd(a,b) denotes the greatest common divisor between a and b, and lcm(a,b) denotes the least common multiple between a and b)

In our case, we are given that
`a\cdot b = 44` and that
`lcm(a,b)=22`. Plugging that in into our identity, we get:

`44=gcd(a,b)\cdot 22`

And so solving for
`gcd(a,b)`:

`gcd(a,b)=(44)/(22)=2`