Question

Find a and b such that : GCD(a,b)=14 and LCM(a,b)=280. ( a , b in IN )

Answer 1

We can write
a = 14p and
b = 14q
where p and q are co-prime.

Then
14pq = 280 => pq = 20.

Choose p = 4 and q = 5.

Then a = 14p = 56
b = 14q = 70

You can verify these values of a and b do indeed have the desired properties.

Answer 2

Damn I'm always too late to be the first to answer a question:)