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

Answer:

2

Step-by-step 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 $gcd(a,b)$:

$gcd(a,b)=\frac{44}{22}=2$