Question

sa se determine cel mai mic nr natural care împărțit la 20,30,45 da restul17,27 ,42

Answer 1

n : 20 = x rest 17 => n = 20x+17 |+3

n : 30 = y rest 27 => n = 30y + 27 |+3

n : 45 = z rest 42 => n = 45z + 42 |+3


=> n + 3 = 20(x + 1)

=> n + 3 = 30(y + 1)

=> n + 3 = 45(z + 1)


20 = 2^2 × 5

30 = 2 × 5 × 3

45 = 3^2 × 5
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cmmmc = 2^2 × 3^2 × 5 = 4 × 9 × 5 = 180


n + 3 = 180

n = 180 - 3

n = 177 (numarul cautat )
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177 : 20 = 8 rest 17

177 : 30 = 5 rest 27

177 : 45 = 3 rest 42