Question

Aflati cel mai mic numar natural care impartit la numerlee 15,20si 45 da, de fiecare data ,un cat diferit de 0 si restul 13 ( sa imi explicati sa inteleg, va rog)

Answer 1

n : 15 = c1 +13 (c1 este catul) =>  n = 15c1 + 13 => n - 13 = 15c1
n : 20 = c2 +13 => n = 20c2 + 13 => n - 13 = 20c2 
n : 45 = c3 + 13 = > n = 45c3 + 13 = > n - 13 = 45c2
n -13 =>  [15,20,45] = 180 
n - 13 = 180
n = 180 + 13 
n = 193 
193 : 15 = 12 rest 13
193 : 20 = 9 rest 13
193 : 45 = 4 rest 13

Answer 2

a:15=C1 rest 13⇒a=15xC1+13⇒a=15C1+13⇒a-13=15C1
a:20=C2 rest 13⇒a=20xC2+13⇒a=20C2+13⇒a-13=20C2
a:45=C3 rest 13⇒a=45xC3+13⇒a=45C3+13⇒a-13=45C3

C1,C2,C3=caturi

Aflam cel mai mic multiplu comun al numerelor 15,20 si 45
15=3x5
20=2²x5
45=3²x5
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[15,20,45]=2²x3²x5=4x9x5=180

a-13=180⇒a=180+13⇒a=193 este cel mai mic nr.

Proba:
193:15=12 rest 13
193:20=9 rest 13
193:45=4 rest 13