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How many ordered pairs of positive integers (x,y) satisfy LCM(x,y)=400? 

 May 3, 2020
 #1
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+1

a=1; b=1;c=lcm(a, b); d=gcd(a, b);if(c==400, goto5, goto6);print"LCM of",a,"and", b,"=",c; a++;if(a<200, goto2, 0);a=1;b++;if(b<200, goto2, discard=0;

 

LCM of 25 and 16 = 400
LCM of 50 and 16 = 400
LCM of 100 and 16 = 400
LCM of 16 and 25 = 400
LCM of 80 and 25 = 400
LCM of 16 and 50 = 400
LCM of 80 and 50 = 400
LCM of 25 and 80 = 400
LCM of 50 and 80 = 400
LCM of 100 and 80 = 400
LCM of 16 and 100 = 400
LCM of 80 and 100 = 400

 May 3, 2020
 #2
avatar+30086 
+3

How about  

1 and 400

2 and 400

4 and 400

5 and 400

...

 

I get 45 in total; assuming (1, 400) is different from (400, 1) etc.

Alan  May 3, 2020

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