This question is really simple if you focus on this part
“The sum of any two is divisible by the third”
⟹⟹ Pairwise, the numbers must have a GCD greater than one.
Let this GCD be xx.
The first three easiest numbers I can think of are x,2xx,2x and 3x3x
Because
gcd(x,2x)=gcd(2x,3x)=gcd(3x,x)=xgcd(x,2x)=gcd(2x,3x)=gcd(3x,x)=x
The numbers sum to 9696
⟹x+2x+3x=96⟹x+2x+3x=96
⟹6x=96⟹6x=96
⟹x=16⟹x=16
The largest number is 3x=3×16=483x=3×16=48
Thanks for the A2A
