330 and 450.

We prime factor 330

330 = 2*165 = 2*3*55 = 2*3*5*11

We prime factor 450

450 = 2*225 = 2*3*75 = 2*3*3*25 = 2*3*3*5*5

Line the prime factors up in columns of like factors like this:

330 = 2*3* *5* *11
450 = 2*3*3*5*5
------------------
HCF = 2*3  *5      = 30  <-- bring down only the factors that are on both lines
                             and multiply them.  

330 = 2*3* *5* *11
450 = 2*3*3*5*5
------------------
LCM = 2*3*3*5*5*11 = 4950  <-- bring down all the factors that are on either
                               line and multiply them.

Both will buzz together in 4950 seconds. Divide by 60. Get 82.5 minutes.
Divide by 60 again. Get 1.375 hours.  The decimal part, 0.375 times 60 
is 22.5 minutes.  So they'll buzz together in 1 hour and 22 and a half 
minutes after 1:00pm. That's 2:22:30pm.

Edwin