Greatest common divisor and least common multiple: building blocks

[@godchild7490]

Love this lots.....it really helped me with my math work

[@jamesedwards6173]

I've liked puzzles my whole life, and this is one of my favorites (encountered long, long ago), which this video reminded me of. There are two integers, A and B; both are greater than 1. Mathematician S knows their sum. Mathematician P knows their product. (All they know otherwise is what you’ve just been told.) The following conversation ensues. S says to P: "You don't know A and B." P says to S: "Now I do know A and B." S says to P: "Now I know A and B, too." What are the values of A and B (that result in a minimal sum)?

[@atifachaudhry]

The example at 8:21 of gcd of the two large numbers is stated as 7, yet both these numbers are even, so the gcd should be even.

[@martinjaskulla5688]

Amazing!

[@sidharthgopalakrishnan6718]

Regarding the pop quiz question. How is it a yes ? Let me show using a example. For example if I take 6 and 9 , 6 = 2 x 3 9 = 3 x 3 hence gcd is 3 but as per your proposition ANY other divisor of a and b ie 2 must also divide gcd ( 6,9) which is false so am I mis understanding your proposition or did you mean ANY common divisor ? Great explanation btw it is really intuitive.

[@marthanelis225]

I think it has to be a common divisor, so 2 should be a divisor of 6 AND 9 to be a divisor of the greatest common divisor. Since 2 isn't a divisor of 9, it indeed does not divide the gcd (6,9)