Question

a)determinati cel mai mic nr natural care impartit pe rand la nr 12 si 15 da resturile 5 si respective 8

b)det cel mai mic nr nat care impartit la nr 24 da restul 10,si impartit la 36 da restul 22

Answer 1

a) x:12 =c1 rest 5
x= M₁₂ +5
x=M₁₂ +12-7
x=M₁₂ -7

x:15=c2 rest 8
x=M₁₅ +8
x=M₁₅ +15 -7
x=M₁₅ -7

x=[M₁₂;M₁₅]-7
x-cel mai mic

12=2² *3
15=3*5
[12;15]= 2² *3 *5= 60

x=60-7
x=53

b)x:24=c1 rest 10
x=M₂₄ +10
x=M₂₄ +24-14
x=M₂₄ -14

x:36=c2 rest 22
x=M₃₆ +22
x=M₃₆ +36-14
x=M₃₆ -14

x=[M₂₄;M₃₆]-14
x-cel mai mic

24=2³ *3
36=2² *3²

[24;36]= 2³ * 3²= 8*9=72

x=72-14
x=58