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LCM and GCD Crossed Value Derivation (Posted on 2024-01-11)

Let each of x and y is a nonnegative integer such that:
x + 3y - 5 = 2*LCM(x,y) - 11*GCD(x,y)
Find the maximum possible value of x+y

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer findings

| Comment 1 of 3

for tot=2:10000

for x=1:tot-1

y=tot-x;

if x+3*y-5==2*lcm(x,y)-11*gcd(x,y)

disp([x,y,tot])

end

finds only

     x     y   x+y
     9     1    10
    65     5    70

making the max 70.

Posted by Charlie on 2024-01-11 08:57:47

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