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The greatest common divisor of two integers is (x+4) and their least common multiple is x(x+4), where x is a positive integer. If one of the integers is 24, what is the smallest possible value of the other one?

 Dec 24, 2020
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a=1; b=1; if(gcd(24 , b)==(a + 4) and lcm(24,b)==a*(a+4), goto loop, goto next);loop:printa, b;print gcd(24, b);print lcm(24,b);next: a++;if(a<1000, goto2, 0);a=1;b++;if(b<1000, goto2, discard=0; 

 

OUTPUT:

 

x = 20   and   GCD =20 +4 =24   and   LCM =20*(20 + 4) = 480

 

The smallest possible value of 2nd number = 480, so that:

GCD[24, 480] == 24   and   LCM[24, 480] ==480, which agrees with the value of x ==20.

 Dec 24, 2020

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