Difference between revisions of "2018 AMC 10B Problems/Problem 23"
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Revision as of 14:35, 16 February 2018
23. How many ordered pairs 
of positive integers satisfy the equation
![\[a\cdot b + 63 = 20\cdot \text{lcm}(a, b) + 12\cdot\text{gcd}(a,b),\]](http://latex.artofproblemsolving.com/1/8/d/18dfc63240b01569b535ba05a0d53841ad6cfe8b.png)
where 
denotes the greatest common divisor of 
and 
, and 
denotes their least common multiple?
