Question

determinați cel mai mic numar natural care împărțit la 18,24,28 da catul nenul si restul 11,17, respectiv 21
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Answer 1

n:18=a r11

n:24=b r17

n:28=c r21

n=18a+11 | +7

n=24b+17 | +7

n=28c+21 | +7

n+7=18a+18

n+7=24b+24

n+7=28c+28

n+7=18(a+1) => n+7 multiplu 18

n+7=24(b+1) => n+7 multiplu 24

n+7=28(c+1) => n+7 multiplu 28

=>

18=2*3^2

24=2^3*3

28=2^2*7

[18, 24, 28]=2^3*3^2*7= 504

n+7=504

n=497

_____

Answer 2

N:18=a r 11
N:24=b r17
N:28=c r21

N=18a+11 |+7
N=24b+17 |+7
N=28c+21 |+7

N+7=18a+18
N+7=24b+24
N+7=28c+28

N+7=18(a+1)
N+7=24(b+1)
N+7=28(c+1)
Rezulta ca :
18=2•3^2
24=2^3•3
28=2^2•7

[18,24,28]=2^3•3^2•7=504
N+7 = 504
N=497
SPER CA TE-AM AJUTATT :) spor!