Answer:
2
Step-by-step explanation:
For any positive numbers a,b we always have the following identity:
[tex]a\cdot b=gcd(a,b)\cdot lcm(a,b)[/tex]
(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 [tex]a\cdot b = 44[/tex] and that [tex]lcm(a,b)=22[/tex]. Plugging that in into our identity, we get:
[tex]44=gcd(a,b)\cdot 22[/tex]
And so solving for [tex]gcd(a,b)[/tex]:
[tex]gcd(a,b)=\frac{44}{22}=2[/tex]
