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Katena32 [7]
3 years ago
8

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

sor?
Mathematics
1 answer:
swat323 years ago
5 0

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

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