LCD/GCD Problem-Solving

The other integer is 55.

The least common multiple will be 3*3*5*x

The highest common factor is  some factor of 45

so

\(\frac{3*3*5* \boxed{x} }{\text{some factor of 45}}=\frac{33}{1}\\ \frac{3*3*5*\boxed{11}}{\boxed{3*5}}=\frac{3*11}{1}\)

So the least common multiple is 3*3*5*11

The highest common factor is  3*5

so they are both multiples of 15 and ours must be a multiple of 11 as well ... 3*5*11=165

So I think the two numbers are  45 and 165

a=1; b=45;c=lcm(a, b); d=gcd(a, b);if(lcm(a,b)/gcd(a,b)==33, goto5, goto7);print"LCM of",a,"and", b,"=",c;print"GCD of",a,"and", b,"=",d; a++;if(a<200, goto2, 0)

LCM of 165 and 45 = 495
GCD of 165 and 45 = 15