Solving for (ab,ac,bc) = 1: Where Am I Going Wrong?

[1+1=1]

i have this one ? and it is bugging me ! show that a,b,c = to (ab,ac,bc)[a,b,c]. () = to the gcd and [] = to the lcm. does that notation mean multiply the numbers together? i mean i started out saying this...

(ab,ac,bc) = 1, so there exist a p prime s.t. p divides ab, p divides ac, and p divides bc. so if p divides ac, then p HAS to divide the other two, right? can anyone show me where i am going wrong and point me in the right direction? thank you all!

 

[AKG]

i have this one ? and it is bugging me ! show that a,b,c = to (ab,ac,bc)[a,b,c].

What does that mean, specifically, "a,b,c = "? Do you mean all three numbers, a, b, and c equal the right side?

(ab,ac,bc) = 1

Why would this be true?

 

[HallsofIvy]

Okay, (a,b,c) is the gdc and [abc] is the lcm but what does a,b,c on the left side of the equation mean? I thought at first that you had forgotten the "[" and meant [a,b,c] but then it's not true. Do you mean a*b*b= (a,b,c)*[a,b,c]?