# Difference between revisions of "2020 CIME II Problems/Problem 12"

Matboy-123 (talk | contribs) (Created page with "How to do this ??") |
Dark adonis (talk | contribs) (Putting in an actual solution) |
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− | + | Note that the <math>lcm(gcd(a,b),c)</math> and its iterations are all divisible by 180. This implies that 2 of <math>a,b,c</math> are divisible by 4, 2 are divisible by 9 and 2 are divisible by 5. | |

+ | <cmath>a,b,c = d 20, e 36, f 45</cmath> | ||

+ | |||

+ | Next we note that iterations are 180,<math>2\times 180</math>,<math>3 \times 180</math>. This implies that <math>d</math> or <math>e</math> must have an additional factor of 2 and <math>e</math> or <math>f</math> must have an additional factor of 3. The sum is minimized if d=2 and e=3 and f=1. | ||

+ | |||

+ | <cmath>a,b,c = 40,45,108</cmath> | ||

+ | <cmath>a+b+c = 193</cmath> |

## Revision as of 09:20, 19 January 2021

Note that the and its iterations are all divisible by 180. This implies that 2 of are divisible by 4, 2 are divisible by 9 and 2 are divisible by 5.

Next we note that iterations are 180,,. This implies that or must have an additional factor of 2 and or must have an additional factor of 3. The sum is minimized if d=2 and e=3 and f=1.