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x, y, and z are positive integers such that gcd(x,y,z)=14 and lcm(x,y,z)=630. What is the smallest possible value of x + y + z?

 Sep 23, 2020
 #1
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The smallest possible value of x + y + z is 162.

 Sep 23, 2020
 #2
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x=1;p=0; y=1;z=1;n=lcm(x, y, z);m=gcd(x, y, z);if(n==630 and m==14, goto loop, goto next);loop:p=p+1;printp," =",x,y,z;next:x++;if(x<200, goto4,0);x=1;y++;if(y<200, goto4, 0);x=1;y=1;z++;if(z<200, goto4,0)

 

OUTPUT: x = 14,  y = 70,  z = 126. x + y + z =14 + 70 + 126 = 210

 Sep 23, 2020

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